R Notebook
Data Science Homework - Homework assignment for Data Scientist candidate
Loading the needed libraries and setting the working directory
library(tidyverse)
[30m-- [1mAttaching packages[22m --------------------------------------- tidyverse 1.2.1 --[39m
[30m[32mv[30m [34mggplot2[30m 2.2.1 [32mv[30m [34mpurrr [30m 0.2.5
[32mv[30m [34mtibble [30m 1.4.2 [32mv[30m [34mdplyr [30m 0.7.5
[32mv[30m [34mtidyr [30m 0.8.1 [32mv[30m [34mstringr[30m 1.3.1
[32mv[30m [34mreadr [30m 1.1.1 [32mv[30m [34mforcats[30m 0.3.0[39m
[30m-- [1mConflicts[22m ------------------------------------------ tidyverse_conflicts() --
[31mx[30m [34mdplyr[30m::[32mfilter()[30m masks [34mstats[30m::filter()
[31mx[30m [34mdplyr[30m::[32mlag()[30m masks [34mstats[30m::lag()[39mlibrary(lubridate)
Attaching package: <U+393C><U+3E31>lubridate<U+393C><U+3E32>
The following object is masked from <U+393C><U+3E31>package:base<U+393C><U+3E32>:
dateImporting the data from the zip file
order <- read.table(unz("data.zip", "order.csv"), header=T, quote="\"", sep=",")
online<- read.table(unz("data.zip", "online.csv"), header=T, quote="\"", sep=",")1. Exploration and understanding of the data sets
Order dataset
Lets look at the structure of the data
str(order)'data.frame': 263278 obs. of 6 variables:
$ custno : int 18944 18944 18944 36096 1 6401 25601 57601 2 2 ...
$ ordno : int 64694 114405 28906 62681 1 8187 41198 112311 2 70848 ...
$ orderdate: Factor w/ 149482 levels "2016-01-01 05:05:14",..: 44835 68024 67301 7798 75039 63162 88311 58274 12156 4041 ...
$ prodcat2 : int NA NA NA NA NA NA NA NA NA NA ...
$ prodcat1 : int 1 1 1 1 1 1 1 1 1 1 ...
$ revenue : num 53.3 0.1 141.66 36.82 8.35 ...we can see that the custno, ordno, prodcat2, prodcat1 are integer but should be factors. Also, orderdate is a factor which should be a Datetime column. Changing the data type of these columns.
order[c('custno','ordno','prodcat1','prodcat2')] <- lapply(order[c('custno','ordno','prodcat1','prodcat2')], factor) ## as.factor() could also be used
order$orderdate <- strptime(x = as.character(order$orderdate),
format = "%Y-%m-%d %H:%M:%S")
order$orderdate <- as.POSIXct(order$orderdate, tz = "", format="%Y-%m-%d %H:%M:%S")
str(order)'data.frame': 263278 obs. of 6 variables:
$ custno : Factor w/ 70264 levels "1","2","3","4",..: 18898 18898 18898 35970 1 6382 25539 57238 2 2 ...
$ ordno : Factor w/ 149717 levels "1","2","3","4",..: 64382 113630 28757 62375 1 8123 41017 111562 2 70445 ...
$ orderdate: POSIXct, format: "2016-11-27 20:57:20" "2017-04-29 20:18:04" "2017-04-23 21:31:03" "2016-02-25 07:16:33" ...
$ prodcat2 : Factor w/ 251 levels "2","3","4","5",..: NA NA NA NA NA NA NA NA NA NA ...
$ prodcat1 : Factor w/ 6 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ...
$ revenue : num 53.3 0.1 141.66 36.82 8.35 ...Now lets look at the summary of the data.
summary(order) custno ordno orderdate prodcat2 prodcat1 revenue
56 : 626 6076 : 26 Min. :2016-01-01 05:05:14 3 : 40908 1:48672 Min. : 0.00
2758 : 451 4803 : 21 1st Qu.:2016-09-28 11:22:56 4 : 15797 2:88684 1st Qu.: 37.43
2511 : 368 5207 : 20 Median :2017-06-25 08:56:10 13 : 13567 3:44019 Median : 74.93
1055 : 350 23233 : 19 Mean :2017-06-29 11:35:41 16 : 13470 4:46681 Mean : 74.94
709 : 345 28041 : 19 3rd Qu.:2018-03-25 09:39:11 11 : 13400 5:11180 3rd Qu.:112.28
3844 : 345 23907 : 17 Max. :2019-01-02 23:54:58 (Other):164313 7:24042 Max. :150.00
(Other):260793 (Other):263156 NA's : 1823 We can see that we have the order data for years 2016, 2017, and 2018. We can also see that there are some missing values in prodcat2.
Lets explore at prodcat2
length(unique(order$prodcat2))[1] 252We have 252 levels in the prodcat2 categorical variable. Lets try to understand the mapping between prodcat1 and prodcat2
tab<-table(order$prodcat2,order$prodcat1)
head(tab,50)
1 2 3 4 5 7
2 0 5148 0 0 0 0
3 0 40908 0 0 0 0
4 0 15797 0 0 0 0
5 0 12946 0 0 0 0
6 0 0 5393 0 0 0
7 0 2294 0 0 0 0
8 0 0 133 0 0 0
9 0 0 12671 0 0 0
10 0 570 0 0 0 0
11 13400 0 0 0 0 0
12 1891 0 0 0 0 0
13 0 0 0 13567 0 0
14 4251 0 0 0 0 0
15 0 0 0 730 0 0
16 0 0 0 13470 0 0
17 0 0 0 0 127 0
18 0 0 0 2758 0 0
19 926 0 0 0 0 0
20 0 0 0 0 1081 0
21 906 0 0 0 0 0
23 0 30 0 0 0 0
24 461 0 0 0 0 0
25 0 0 0 0 0 4773
26 0 0 266 0 0 0
27 0 0 3535 0 0 0
28 0 0 0 0 0 4785
30 0 0 4217 0 0 0
32 0 0 216 0 0 0
33 303 0 0 0 0 0
34 55 0 0 0 0 0
35 0 735 0 0 0 0
38 0 0 0 0 6552 0
39 0 0 0 0 2321 0
40 1344 0 0 0 0 0
41 1156 0 0 0 0 0
42 0 2282 0 0 0 0
43 0 0 2400 0 0 0
44 0 0 1647 0 0 0
45 0 0 2357 0 0 0
46 0 217 0 0 0 0
47 0 0 0 0 0 208
48 0 0 472 0 0 0
49 0 0 279 0 0 0
50 0 0 0 0 0 2493
51 0 0 798 0 0 0
52 0 0 182 0 0 0
53 0 0 33 0 0 0
54 0 0 0 1090 0 0
55 0 138 0 0 0 0
56 0 0 99 0 0 0There are also NA’s in the prodcat2.
summary(order$prodcat2) 3 4 13 16 11 5 89 9 78 38 6 2 28 25
40908 15797 13567 13470 13400 12946 12772 12671 8341 6552 5393 5148 4785 4773
14 30 110 27 96 18 58 119 50 43 45 39 7 42
4251 4217 3954 3535 3520 2758 2596 2572 2493 2400 2357 2321 2294 2282
59 12 107 44 77 145 75 40 147 41 54 20 85 99
2068 1891 1673 1647 1604 1457 1448 1344 1340 1156 1090 1081 960 960
19 213 21 51 70 93 35 15 69 131 74 155 97 10
926 922 906 798 766 745 735 730 726 711 656 584 577 570
116 80 48 115 24 180 149 169 67 113 168 195 132 91
522 511 472 470 461 451 444 425 385 384 374 356 341 324
33 94 134 49 57 66 171 26 165 138 92 144 62 73
303 291 284 279 277 273 271 266 264 263 259 241 231 223
174 46 114 32 47 90 140 79 72 214 52 146 183 112
220 217 217 216 208 202 202 201 193 187 182 180 179 173
(Other) NA's
6889 1823 There are 1823 NA’s in the prodcat2 field. We could impute these values using statistical methods. However, given the time-constraint, we won’t dive deep into prodcat2.
Lets first understand the level of the data. Intuitively, it looks like that the data is at product level. Lets check that by aggregating data.
level_ord<- order %>% group_by(custno,ordno,orderdate,prodcat1,prodcat2) %>% summarise(cnt=n()) %>% arrange(desc(cnt))
head(level_ord)We can see that for custno 9 and ordno 23204, we are getting the cnt of more than 1 for each combination of prodcat1 and prodcat2. Lets look at the order data for this case
order %>% filter(custno==9,ordno==23204) custno ordno orderdate prodcat2 prodcat1 revenue
1 9 23204 2016-01-03 18:27:48 3 2 1.27
2 9 23204 2016-01-03 18:27:48 3 2 33.11
3 9 23204 2016-01-03 18:27:48 110 2 90.07
4 9 23204 2016-01-03 18:27:48 110 2 131.97We clearly see from the above example that the data is at product level. Lets get it at order and prodcat1 level.
order_agg<- order %>% group_by(custno,ordno,orderdate,prodcat1) %>% summarise(revenue = sum(revenue), num_prod = n())
head(order_agg,10)Lets look at revenue.
summary(order$revenue) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.00 37.43 74.93 74.94 112.28 150.00 hist(order$revenue,breaks = 30)
We can see from the histogram that revenue is uniformly distributed. Lets check revenue and ordersize across different prodcat1 and customers
order %>% group_by(prodcat1) %>% summarise(avg_rev_per_product=mean(revenue),total_rev=sum(revenue),num_orders=length(unique(ordno)),cnt_cust=length(unique(custno)))[38;5;246m# A tibble: 6 x 5[39m
prodcat1 avg_rev_per_product total_rev num_orders cnt_cust
[3m[38;5;246m<fct>[39m[23m [3m[38;5;246m<dbl>[39m[23m [3m[38;5;246m<dbl>[39m[23m [3m[38;5;246m<int>[39m[23m [3m[38;5;246m<int>[39m[23m
[38;5;250m1[39m 1 74.9 3[4m6[24m[4m4[24m[4m4[24m599. [4m2[24m[4m9[24m875 [4m1[24m[4m8[24m241
[38;5;250m2[39m 2 75.2 6[4m6[24m[4m6[24m[4m9[24m793. [4m5[24m[4m3[24m510 [4m3[24m[4m0[24m260
[38;5;250m3[39m 3 74.7 3[4m2[24m[4m9[24m[4m0[24m307. [4m3[24m[4m6[24m538 [4m1[24m[4m7[24m614
[38;5;250m4[39m 4 74.7 3[4m4[24m[4m8[24m[4m4[24m911. [4m2[24m[4m8[24m188 [4m1[24m[4m7[24m775
[38;5;250m5[39m 5 75.7 [4m8[24m[4m4[24m[4m6[24m064. [4m9[24m724 [4m4[24m684
[38;5;250m6[39m 7 74.6 1[4m7[24m[4m9[24m[4m4[24m195. [4m2[24m[4m1[24m669 [4m1[24m[4m0[24m670From the above data we can see that the prodcat1=1 has the highest sales volume both in terms of revenue, number of orders as well as number of customers, whereas prodcat1=5 has the lowest.
Lets look at trend in revenue with time
library(lubridate)
order %>% mutate(Year_Month=format(as.Date(orderdate), "%Y-%m")) %>% group_by(Year_Month) %>% summarise(revenue=sum(revenue)) %>% ggplot(aes(x=Year_Month,y=revenue)) + geom_bar(stat='identity')+
xlab('orderdate')+ylab('Revenue')+ theme(axis.text.x = element_text(angle = 90, hjust = 1))#+ggtitle("Cumulative")
We can see a seasonlaity here. The Revenue peaks during the months of Dec and Jan. It then drops during the month of Feb and starts rising again and reaches another peak around May-June and then plunges in Oct. Then it rises again and peaks in Dec-Jan. The highest revenue was earned in Jan-2017 and lowest in Oct-2018.Lets break it down across product category and see if we get any seasonality across prodcat1.
order %>% mutate(Year_Month=format(as.Date(orderdate), "%Y-%m")) %>% group_by(Year_Month,prodcat1) %>% summarise(revenue=sum(revenue)) %>% ggplot(aes(x=Year_Month,y=revenue,color=prodcat1,group=prodcat1)) + geom_line()+ facet_wrap(~prodcat1,nrow=3, scales = 'free') +
xlab('orderdate')+ylab('Revenue')+ theme(axis.text.x = element_text(angle = 90, hjust = 1))#+ggtitle("Cumulative")
We can see a seasonality across all the prodcat1 similar to the overall revenue category
We expect a similar trend for num_products ordered. Lets calculate the correlation between revenue and number of products ordered.
cor(order_agg$revenue,order_agg$num_prod)[1] 0.7414783The two fields are highly correlated which is evident from the scatter-plot given below
order_agg %>% ggplot(aes(x=revenue,y=num_prod)) + geom_point()
Lets look at the scatterplot across each product category and calculate the correlation at that level.
order_agg %>% ggplot(aes(x=revenue,y=num_prod)) + geom_point()+ facet_wrap(~prodcat1,nrow=3, scales = 'free')
order_agg %>% group_by(prodcat1) %>% summarise(cor_rev_prod=cor(revenue,num_prod))[38;5;246m# A tibble: 6 x 2[39m
prodcat1 cor_rev_prod
[3m[38;5;246m<fct>[39m[23m [3m[38;5;246m<dbl>[39m[23m
[38;5;250m1[39m 1 0.710
[38;5;250m2[39m 2 0.796
[38;5;250m3[39m 3 0.642
[38;5;250m4[39m 4 0.690
[38;5;250m5[39m 5 0.531
[38;5;250m6[39m 7 0.557The correlation across each prodcat1 is high.
Online dataset
Lets look at the structure of the data
str(online)'data.frame': 954774 obs. of 7 variables:
$ session : int 419542 3030130 2638740 880408 2612179 880953 418956 281663 26191 1363670 ...
$ visitor : int 140970 14501 419353 90673 191542 419268 14938 419163 419163 14464 ...
$ dt : Factor w/ 942579 levels "2016-01-01 00:00:08",..: 302552 854890 652906 833133 156326 222492 891922 466197 367097 644408 ...
$ custno : int 3840 70400 21248 39168 47616 47616 47872 49920 49920 54784 ...
$ category: int 1 1 1 1 1 1 1 1 1 1 ...
$ event1 : int NA NA NA NA NA NA NA NA NA NA ...
$ event2 : int 1 1 1 1 1 1 1 1 1 1 ...The categorical columns custno, category, event1, event2, session, and visitor are in integer and the dt column should be of datetime datetype.
online[c('session','visitor','custno','category','event1','event2')] <- lapply(online[c('session','visitor','custno','category','event1','event2')], factor) ## as.factor() could also be used
online$dt <- strptime(x = as.character(online$dt),
format = "%Y-%m-%d %H:%M:%S")
online$dt <- as.POSIXct(online$dt, tz = "", format="%Y-%m-%d %H:%M:%S")
str(online)'data.frame': 954774 obs. of 7 variables:
$ session : Factor w/ 850235 levels "2","3","6","9",..: 93667 680561 591950 197824 586838 197906 93569 62818 6501 307342 ...
$ visitor : Factor w/ 259950 levels "1","3","5","6",..: 73857 9086 217101 48286 99883 217040 9388 216958 216958 9058 ...
$ dt : POSIXct, format: "2016-09-16 05:03:23" "2017-11-13 04:58:12" "2017-05-24 16:10:38" "2017-10-28 13:42:38" ...
$ custno : Factor w/ 57584 levels "6","7","8","9",..: 3173 56713 17326 31495 38364 38364 38560 40169 40169 43840 ...
$ category: Factor w/ 3 levels "1","2","3": 1 1 1 1 1 1 1 1 1 1 ...
$ event1 : Factor w/ 10 levels "1","2","4","5",..: NA NA NA NA NA NA NA NA NA NA ...
$ event2 : Factor w/ 10 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ...Lets look at the summary of the data
summary(online) session visitor dt custno category event1
72733 : 5 328620 : 440 Min. :2016-01-01 00:00:08 713 : 855 1: 52964 1 : 51567
157423 : 5 178635 : 310 1st Qu.:2016-07-25 15:01:06 10785 : 505 2:194890 4 : 23858
161973 : 5 227902 : 281 Median :2016-12-27 07:21:38 34515 : 479 3:706920 2 : 23312
692928 : 5 53505 : 276 Mean :2017-01-10 19:15:08 336 : 473 11 : 20586
811699 : 5 279881 : 276 3rd Qu.:2017-07-10 18:51:39 28702 : 470 6 : 16537
1178030: 5 328827 : 254 Max. :2017-12-31 23:58:05 57148 : 425 (Other): 29068
(Other):954744 (Other):952937 (Other):951567 NA's :789846
event2
7 :367857
3 :129795
8 :122402
4 : 94230
1 : 86496
9 : 52145
(Other):101849 We can see that the duration of the online data is from Jan-2016 to Dec-2017. We have 3 levels in online browsing category and multiple levels in event1 and event2. Lets first compare the number of customers in online vs order.
length(unique(online$custno))[1] 57584length(unique(order$custno))[1] 70264There are 57584 customers in online and 70264 customers in the order dataset. Getting a list of customers common to both the datasets
common_cust<-unique(order[which(order$custno %in% unique(online$custno)),]$custno)
length(common_cust)[1] 56764Lets calculate online activity across each of online browsing categories.
online %>% group_by(category) %>% summarise(activity=n(),unique_sessions=length(unique(session)),num_cust=length(unique(custno)))[38;5;246m# A tibble: 3 x 4[39m
category activity unique_sessions num_cust
[3m[38;5;246m<fct>[39m[23m [3m[38;5;246m<int>[39m[23m [3m[38;5;246m<int>[39m[23m [3m[38;5;246m<int>[39m[23m
[38;5;250m1[39m 1 [4m5[24m[4m2[24m964 [4m4[24m[4m7[24m228 [4m1[24m[4m0[24m001
[38;5;250m2[39m 2 [4m1[24m[4m9[24m[4m4[24m890 [4m1[24m[4m7[24m[4m5[24m809 [4m3[24m[4m0[24m466
[38;5;250m3[39m 3 [4m7[24m[4m0[24m[4m6[24m920 [4m6[24m[4m2[24m[4m7[24m275 [4m5[24m[4m1[24m222Here activity means any sort of activity, be it creation of session, change in event1 or event2 etc. Unique sessions is the count of unique sessions created on each category and new_cust is the number of unique customers that used that category. Here, online browsing category could mean which device or what channel is used by the customer to browse the website.
Moving onto event1, we can see that majority of the values in that field are null
prop.table(table(online$event1,useNA = "ifany"))*100
1 2 4 5 6 7 8 9 10 11
5.4009640 2.4416249 2.4988112 0.1542773 1.7320329 1.1956756 1.1485441 0.4178999 0.1280931 2.1561123
<NA>
82.7259645 83% of the values are null in event1. We will assume here that all the null values in event1 belong to one class which is class 0.
levels(online$event1) [1] "1" "2" "4" "5" "6" "7" "8" "9" "10" "11"online$event1<-factor(ifelse(is.na(online$event1), 0, paste(online$event1)), levels = c(levels(online$event1), 0))
levels(online$event1) [1] "1" "2" "4" "5" "6" "7" "8" "9" "10" "11" "0" prop.table(table(online$event1))*100
1 2 4 5 6 7 8 9 10 11
5.4009640 2.4416249 2.4988112 0.1542773 1.7320329 1.1956756 1.1485441 0.4178999 0.1280931 2.1561123
0
82.7259645 Lets look at event2,
prop.table(table(online$event2,useNA = "ifany"))*100
1 2 3 4 5 6 7 8 9 10
9.0593167 1.6149371 13.5943166 9.8693513 5.0569035 3.1329927 38.5281753 12.8199972 5.4615019 0.8625078 We can see that event2 is a highly imbalanced class with 39% of the data is in class 7 and 14% in class3. Lets look at online activity across each of the class in event2.
online %>% group_by(event2) %>% summarise(activity=n(),unique_sessions=length(unique(session)),num_cust=length(unique(custno)))[38;5;246m# A tibble: 10 x 4[39m
event2 activity unique_sessions num_cust
[3m[38;5;246m<fct>[39m[23m [3m[38;5;246m<int>[39m[23m [3m[38;5;246m<int>[39m[23m [3m[38;5;246m<int>[39m[23m
[38;5;250m 1[39m 1 [4m8[24m[4m6[24m496 [4m8[24m[4m6[24m496 [4m2[24m[4m8[24m945
[38;5;250m 2[39m 2 [4m1[24m[4m5[24m419 [4m1[24m[4m5[24m175 [4m9[24m607
[38;5;250m 3[39m 3 [4m1[24m[4m2[24m[4m9[24m795 [4m1[24m[4m2[24m[4m9[24m788 [4m3[24m[4m4[24m495
[38;5;250m 4[39m 4 [4m9[24m[4m4[24m230 [4m9[24m[4m4[24m123 [4m3[24m[4m2[24m906
[38;5;250m 5[39m 5 [4m4[24m[4m8[24m282 [4m4[24m[4m8[24m023 [4m2[24m[4m1[24m858
[38;5;250m 6[39m 6 [4m2[24m[4m9[24m913 [4m2[24m[4m9[24m873 [4m1[24m[4m4[24m487
[38;5;250m 7[39m 7 [4m3[24m[4m6[24m[4m7[24m857 [4m3[24m[4m5[24m[4m5[24m901 [4m5[24m[4m0[24m696
[38;5;250m 8[39m 8 [4m1[24m[4m2[24m[4m2[24m402 [4m1[24m[4m2[24m[4m2[24m388 [4m3[24m[4m6[24m507
[38;5;250m 9[39m 9 [4m5[24m[4m2[24m145 [4m5[24m[4m2[24m144 [4m2[24m[4m4[24m552
[38;5;250m10[39m 10 [4m8[24m235 [4m8[24m057 [4m3[24m985AS expected, most of the activity is across class7 followed by class3 and class8. However, its still not enough to tell us what the value of each those class means.
Lets look at the time series trends of online activity
online %>% mutate(Year_Month=format(as.Date(dt), "%Y-%m")) %>% group_by(Year_Month) %>% summarise(activity=n(),unique_sessions=length(unique(session)),num_cust=length(unique(custno)))%>% ggplot() + geom_line(aes(x = Year_Month, y = activity, group=1, colour = "activity")) +
geom_line(aes(x = Year_Month, y = unique_sessions, group=2, colour = "unique_sessions")) +
geom_line(aes(x = Year_Month, y = num_cust, group=2, colour = "num_cust"))+ theme(axis.text.x = element_text(angle = 90, hjust = 1))
We will further break it down by browsing category
online %>% mutate(Year_Month=format(as.Date(dt), "%Y-%m")) %>% group_by(Year_Month,category) %>% summarise(activity=n(),unique_sessions=length(unique(session)),num_cust=length(unique(custno)))%>% ggplot() + geom_line(aes(x = Year_Month, y = activity, group=1, colour = "activity")) +
geom_line(aes(x = Year_Month, y = unique_sessions, group=2, colour = "unique_sessions")) +
geom_line(aes(x = Year_Month, y = num_cust, group=2, colour = "num_cust"))+
facet_wrap(~category, nrow=2,scales = 'free') +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
Lets break down online activity by event2.
online %>% mutate(Year_Month=format(as.Date(dt), "%Y-%m")) %>% group_by(Year_Month,event2) %>% summarise(activity=n(),unique_sessions=length(unique(session)),num_cust=length(unique(custno)))%>% ggplot() + geom_line(aes(x = Year_Month, y = activity, group=1, colour = "activity")) +
geom_line(aes(x = Year_Month, y = unique_sessions, group=2, colour = "unique_sessions")) +
geom_line(aes(x = Year_Month, y = num_cust, group=2, colour = "num_cust"))+
facet_wrap(~event2, nrow=5,scales = 'free') +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
From all the online activity plot, we can see a seasonality trend. The online activity starts peaking from Nov till Jan then falls to the lowest in Feb. It then remains pretty steady till Oct. This trend is similar to the one we obtained for revenue and number of orders.
2.Feature engineering
Lets try to understand the level of the data in online dataset.
level_online<-online %>% group_by(session,custno,dt,event1,event2)%>% summarise(cnt=n()) %>% arrange(desc(cnt))
head(level_online)We can see that each record is uniquely identified at session, customer, datetime, event1, and event2. Lets change the level of the data by spreading the online data on event2
online$val<-1
online_spread_e2<-spread(online,event2,val,fill=0,sep = '_')
head(online_spread_e2) session visitor dt custno category event1 event2_1 event2_2 event2_3 event2_4 event2_5 event2_6
1 419542 140970 2016-09-16 05:03:23 3840 1 0 1 0 0 0 0 0
2 3030130 14501 2017-11-13 04:58:12 70400 1 0 1 0 0 0 0 0
3 2638740 419353 2017-05-24 16:10:38 21248 1 0 1 0 0 0 0 0
4 880408 90673 2017-10-28 13:42:38 39168 1 0 1 0 0 0 0 0
5 2612179 191542 2016-05-17 06:30:32 47616 1 0 1 0 0 0 0 0
6 880953 419268 2016-07-15 12:36:42 47616 1 0 1 0 0 0 0 0
event2_7 event2_8 event2_9 event2_10
1 0 0 0 0
2 0 0 0 0
3 0 0 0 0
4 0 0 0 0
5 0 0 0 0
6 0 0 0 0online$val<-NULLWe will further spread the online data on key event1.
online_spread_e2$val<-1
online_spread_e2e1<-spread(online_spread_e2,event1,val,fill=0,sep = '_')
head(online_spread_e2e1) session visitor dt custno category event2_1 event2_2 event2_3 event2_4 event2_5 event2_6 event2_7
1 419542 140970 2016-09-16 05:03:23 3840 1 1 0 0 0 0 0 0
2 3030130 14501 2017-11-13 04:58:12 70400 1 1 0 0 0 0 0 0
3 2638740 419353 2017-05-24 16:10:38 21248 1 1 0 0 0 0 0 0
4 880408 90673 2017-10-28 13:42:38 39168 1 1 0 0 0 0 0 0
5 2612179 191542 2016-05-17 06:30:32 47616 1 1 0 0 0 0 0 0
6 880953 419268 2016-07-15 12:36:42 47616 1 1 0 0 0 0 0 0
event2_8 event2_9 event2_10 event1_1 event1_2 event1_4 event1_5 event1_6 event1_7 event1_8 event1_9 event1_10
1 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0 0 0 0
event1_11 event1_0
1 0 1
2 0 1
3 0 1
4 0 1
5 0 1
6 0 1There is also a possibility that a customer can use different browsing categories (for example, custno 6). To account for that we have to spread the data by category as well.
online_spread_e2e1$val<-1
online_spread_e2e1cat<-spread(online_spread_e2e1,category,val,fill=0,sep = '_')
head(online_spread_e2e1cat) session visitor dt custno event2_1 event2_2 event2_3 event2_4 event2_5 event2_6 event2_7 event2_8
1 419542 140970 2016-09-16 05:03:23 3840 1 0 0 0 0 0 0 0
2 3030130 14501 2017-11-13 04:58:12 70400 1 0 0 0 0 0 0 0
3 2638740 419353 2017-05-24 16:10:38 21248 1 0 0 0 0 0 0 0
4 880408 90673 2017-10-28 13:42:38 39168 1 0 0 0 0 0 0 0
5 2612179 191542 2016-05-17 06:30:32 47616 1 0 0 0 0 0 0 0
6 880953 419268 2016-07-15 12:36:42 47616 1 0 0 0 0 0 0 0
event2_9 event2_10 event1_1 event1_2 event1_4 event1_5 event1_6 event1_7 event1_8 event1_9 event1_10 event1_11
1 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0 0 0 0
event1_0 category_1 category_2 category_3
1 1 1 0 0
2 1 1 0 0
3 1 1 0 0
4 1 1 0 0
5 1 1 0 0
6 1 1 0 0Now, we will engineer features from Order data. One set of important features are is the revenue made by a customer on the last order of the same product category as well as and the number number of items ordered the last time. I have created those features below
order_agg<- order_agg %>% arrange(custno,prodcat1,orderdate,) %>% group_by(custno, prodcat1) %>% mutate(cum_rev=cumsum(revenue), cum_num_prod=cumsum(num_prod))
order_agg$cumrev_till_prev_order <- order_agg$cum_rev - order_agg$revenue
order_agg$cumnum_prod_till_prev_order <- order_agg$cum_num_prod - order_agg$num_prod
order_agg <- order_agg %>% arrange(custno,prodcat1,orderdate) %>%
group_by(custno,prodcat1) %>%
mutate(rev_prev_ord = dplyr::lag(revenue, n = 1, default = 0),num_prod_prev_ord = dplyr::lag(num_prod, n = 1, default = 0))
order_agg[,c("revenue","num_prod","cum_rev","cum_num_prod")]<-NULL
summary(order_agg) custno ordno orderdate prodcat1 cumrev_till_prev_order
56 : 479 1974 : 5 Min. :2016-01-01 05:05:14 1:29875 Min. : 0.0
2758 : 347 2794 : 5 1st Qu.:2016-09-25 19:15:03 2:53510 1st Qu.: 0.0
1055 : 321 3657 : 5 Median :2017-06-17 17:01:47 3:36538 Median : 0.0
1488 : 303 4577 : 5 Mean :2017-06-24 14:26:40 4:28188 Mean : 445.5
1581 : 269 5614 : 5 3rd Qu.:2018-03-17 07:09:34 5: 9724 3rd Qu.: 387.6
3844 : 268 5949 : 5 Max. :2019-01-02 23:54:58 7:21669 Max. :22676.0
(Other):177517 (Other):179474
cumnum_prod_till_prev_order rev_prev_ord num_prod_prev_ord
Min. : 0.000 Min. : 0.00 Min. : 0.0000
1st Qu.: 0.000 1st Qu.: 0.00 1st Qu.: 0.0000
Median : 0.000 Median : 0.00 Median : 0.0000
Mean : 5.976 Mean : 45.24 Mean : 0.6045
3rd Qu.: 5.000 3rd Qu.: 83.79 3rd Qu.: 1.0000
Max. :305.000 Max. :1578.89 Max. :17.0000
The following four metrics are created. 1. cum_rev_till_prev_order: This is the cumulative revenue of a customer till previous order 2. cumnum_prod_till_prev_order: Cumulative number of items till previous order. 3. rev_prev_order: revenue made from previous order 4. num_prod_prev_order: Number of items ordered from previous order
Another important metric would be number of days till last order
order_agg <- order_agg %>% arrange(custno,prodcat1,orderdate) %>%
group_by(custno,prodcat1) %>%
mutate(orderdate_prev_ord = dplyr::lag(orderdate, n = 1, default = NA))
order_agg$num_days_till_last_order <- difftime(order_agg$orderdate, order_agg$orderdate_prev_ord, units="days")
order_agg$orderdate_prev_ord<-NULL
order_agg$num_days_till_last_order <-as.numeric(order_agg$num_days_till_last_order)
summary(order_agg$num_days_till_last_order) Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
0.00 9.65 35.19 100.02 127.97 1081.32 99244 The order aggregate data now looks like.
head(order_agg,10)Now lets join the above data with order_agg data (order data aggregated at order-prodcat1 level). We will join order_agg with prodcat1 on the inequality. Since we are planning to predict prodcat1, we will put order_agg on the left and perform a left join.
joined_df<-left_join(order_agg,online_spread_e2e1cat,by="custno") Column `custno` joining factors with different levels, coercing to character vectorjoined_df[,13:36][is.na(joined_df[,13:36])] <- 0
joined_df$dt<- as.character(joined_df$dt)
joined_df$dt<-ifelse(joined_df$dt>joined_df$orderdate,NA,joined_df$dt)
joined_df$dt <- strptime(x = as.character(joined_df$dt),
format = "%Y-%m-%d %H:%M:%S")
joined_df$dt <- as.POSIXct(joined_df$dt, tz = "", format="%Y-%m-%d %H:%M:%S")
joined_df[c("session","visitor","event2_1","event2_2","event2_3","event2_4","event2_5","event2_6","event2_7","event2_8","event2_9","event2_10","event1_1","event1_2","event1_4","event1_5","event1_6","event1_7","event1_8","event1_9","event1_10","event1_11","event1_0","category_1","category_2","category_3")]<-lapply(joined_df[c("session","visitor","event2_1","event2_2","event2_3","event2_4","event2_5","event2_6","event2_7","event2_8","event2_9","event2_10","event1_1","event1_2","event1_4","event1_5","event1_6","event1_7","event1_8","event1_9","event1_10","event1_11","event1_0","category_1","category_2","category_3")], function(x) ifelse(is.na(joined_df$dt)==TRUE,NA,x))
joined_df<- joined_df %>% filter(orderdate>=dt | is.na(dt)==TRUE)
head(joined_df,20)as you can see for a customer with a given orderno and prodcat1, only the online activity on or before the time of the order is joined. Now lets calculate the difference between orderdate and dt. Note: We are also incluing the order data for which no online data is available
joined_df$date_diff<- difftime(joined_df$orderdate,joined_df$dt,units = 'days')
head(joined_df,20)We are assuming that only the last 30 days of online activity drives buying behaviour. Therefor we will only consider online activities and browsing category that occured 30 days before a transaction.
What we have done above is for date difference greater than 30 days, we have changed the events flags (event2_1, event2_2 etc.) and to browsing category flags to 0 as we are not considering those events to have an impact on the buying behaviour. Now we will aggregate the data by taking the count of each events and categories. This count will be the number of times that event has happened (or browsing category used) in the past 30 days before a transaction.
Now we will aggregate the data to order-prodcat1 level
df<- joined_df_new %>% group_by(custno,ordno,orderdate,prodcat1,cumrev_till_prev_order,cumnum_prod_till_prev_order,rev_prev_ord,num_prod_prev_ord,num_days_till_last_order) %>%
summarise(sum_category_1 = sum(category_1),
sum_category_2 = sum(category_2),
sum_category_3 = sum(category_3),
sum_event1_1 = sum(event1_1),
sum_event1_2 = sum(event1_2),
sum_event1_4 = sum(event1_4),
sum_event1_5 = sum(event1_5),
sum_event1_6 = sum(event1_6),
sum_event1_7 = sum(event1_7),
sum_event1_8 = sum(event1_8),
sum_event1_9 = sum(event1_9),
sum_event1_10 = sum(event1_10),
sum_event1_11 = sum(event1_11),
sum_event2_1 = sum(event2_1),
sum_event2_2 = sum(event2_2),
sum_event2_3 = sum(event2_3),
sum_event2_4 = sum(event2_4),
sum_event2_5 = sum(event2_5),
sum_event2_6 = sum(event2_6),
sum_event2_7 = sum(event2_7),
sum_event2_8 = sum(event2_8),
sum_event2_9 = sum(event2_9),
sum_event2_10 = sum(event2_10),
avg_date_diff = mean(date_diff,na.rm = TRUE)
)
head(df)Another metric we can include is revenue per product for cumuative value as well as previous orders
df$cumrev_per_prod_till_prev_order <- ifelse(df$cumrev_till_prev_order==0,0,df$cumrev_till_prev_order/df$cumnum_prod_till_prev_order)
df$rev_per_prod_prev_ord <- ifelse(df$rev_prev_ord==0,0,df$rev_prev_ord/df$num_prod_prev_ord)
df[,c('cumrev_till_prev_order','cumnum_prod_till_prev_order','rev_prev_ord','num_prod_prev_ord')]<-NULLdf$avg_date_diff<-as.numeric(df$avg_date_diff)Breaking down orderdate to month, quarter, day-of-week, week of the year and hour
df$order_month<-format(df$orderdate,"%m")
df$order_week_of_year<-strftime(df$orderdate,format="%W")
library(lubridate)
df$order_qtr<-quarter(df$orderdate)
df$order_day_of_week<-weekdays(df$orderdate,abbreviate = TRUE)
df$order_hour_of_day<-format(df$orderdate,"%H")
# converting the above features to factors
df[c('order_month','order_week_of_year','order_qtr','order_day_of_week','order_hour_of_day')] <- lapply(df[c('order_month','order_week_of_year','order_qtr','order_day_of_week','order_hour_of_day')], factor)We have created the folllowing features by manipulating and combining order and online data.
head(df)[38;5;246m# A tibble: 6 x 36[39m
custno ordno orderdate prodcat1 num_days_till_last_order sum_category_1 sum_category_2 sum_category_3
[3m[38;5;246m<chr>[39m[23m [3m[38;5;246m<fct>[39m[23m [3m[38;5;246m<dttm>[39m[23m [3m[38;5;246m<fct>[39m[23m [3m[38;5;246m<dbl>[39m[23m [3m[38;5;246m<dbl>[39m[23m [3m[38;5;246m<dbl>[39m[23m [3m[38;5;246m<dbl>[39m[23m
[38;5;250m1[39m 1 1 2017-06-12 [38;5;246m08:27:59[39m 1 [31mNA[39m 0 0 0
[38;5;250m2[39m 10 10 2017-04-09 [38;5;246m23:38:53[39m 2 [31mNA[39m 0 0 0
[38;5;250m3[39m 100 101 2017-11-22 [38;5;246m04:52:43[39m 1 359. 0 0 0
[38;5;250m4[39m 100 101 2017-11-22 [38;5;246m04:52:43[39m 2 114. 0 0 0
[38;5;250m5[39m 100 4234 2018-12-10 [38;5;246m17:57:38[39m 1 369. 0 0 0
[38;5;250m6[39m 100 21787 2018-07-23 [38;5;246m18:43:40[39m 2 244. 0 0 0
[38;5;246m# ... with 28 more variables: sum_event1_1 [3m[38;5;246m<dbl>[38;5;246m[23m, sum_event1_2 [3m[38;5;246m<dbl>[38;5;246m[23m, sum_event1_4 [3m[38;5;246m<dbl>[38;5;246m[23m, sum_event1_5 [3m[38;5;246m<dbl>[38;5;246m[23m,
# sum_event1_6 [3m[38;5;246m<dbl>[38;5;246m[23m, sum_event1_7 [3m[38;5;246m<dbl>[38;5;246m[23m, sum_event1_8 [3m[38;5;246m<dbl>[38;5;246m[23m, sum_event1_9 [3m[38;5;246m<dbl>[38;5;246m[23m, sum_event1_10 [3m[38;5;246m<dbl>[38;5;246m[23m,
# sum_event1_11 [3m[38;5;246m<dbl>[38;5;246m[23m, sum_event2_1 [3m[38;5;246m<dbl>[38;5;246m[23m, sum_event2_2 [3m[38;5;246m<dbl>[38;5;246m[23m, sum_event2_3 [3m[38;5;246m<dbl>[38;5;246m[23m, sum_event2_4 [3m[38;5;246m<dbl>[38;5;246m[23m,
# sum_event2_5 [3m[38;5;246m<dbl>[38;5;246m[23m, sum_event2_6 [3m[38;5;246m<dbl>[38;5;246m[23m, sum_event2_7 [3m[38;5;246m<dbl>[38;5;246m[23m, sum_event2_8 [3m[38;5;246m<dbl>[38;5;246m[23m, sum_event2_9 [3m[38;5;246m<dbl>[38;5;246m[23m,
# sum_event2_10 [3m[38;5;246m<dbl>[38;5;246m[23m, avg_date_diff [3m[38;5;246m<dbl>[38;5;246m[23m, cumrev_per_prod_till_prev_order [3m[38;5;246m<dbl>[38;5;246m[23m, rev_per_prod_prev_ord [3m[38;5;246m<dbl>[38;5;246m[23m,
# order_month [3m[38;5;246m<fct>[38;5;246m[23m, order_week_of_year [3m[38;5;246m<fct>[38;5;246m[23m, order_qtr [3m[38;5;246m<fct>[38;5;246m[23m, order_day_of_week [3m[38;5;246m<fct>[38;5;246m[23m, order_hour_of_day [3m[38;5;246m<fct>[38;5;246m[23m[39mThe summary of the data is
summary(df) custno ordno orderdate prodcat1 num_days_till_last_order
Length:179504 1974 : 5 Min. :2016-01-01 05:05:14 1:29875 Min. : 0.00
Class :character 2794 : 5 1st Qu.:2016-09-25 19:15:03 2:53510 1st Qu.: 9.65
Mode :character 3657 : 5 Median :2017-06-17 17:01:47 3:36538 Median : 35.19
4577 : 5 Mean :2017-06-24 14:26:40 4:28188 Mean : 100.02
5614 : 5 3rd Qu.:2018-03-17 07:09:34 5: 9724 3rd Qu.: 127.97
5949 : 5 Max. :2019-01-02 23:54:58 7:21669 Max. :1081.32
(Other):179474 NA's :99244
sum_category_1 sum_category_2 sum_category_3 sum_event1_1 sum_event1_2 sum_event1_4
Min. : 0.00000 Min. : 0.0000 Min. : 0.000 Min. : 0.00000 Min. :0.00000 Min. :0.00000
1st Qu.: 0.00000 1st Qu.: 0.0000 1st Qu.: 0.000 1st Qu.: 0.00000 1st Qu.:0.00000 1st Qu.:0.00000
Median : 0.00000 Median : 0.0000 Median : 0.000 Median : 0.00000 Median :0.00000 Median :0.00000
Mean : 0.07668 Mean : 0.3121 Mean : 1.205 Mean : 0.07388 Mean :0.03828 Mean :0.03738
3rd Qu.: 0.00000 3rd Qu.: 0.0000 3rd Qu.: 1.000 3rd Qu.: 0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
Max. :25.00000 Max. :32.0000 Max. :55.000 Max. :12.00000 Max. :9.00000 Max. :8.00000
sum_event1_5 sum_event1_6 sum_event1_7 sum_event1_8 sum_event1_9 sum_event1_10
Min. :0.000000 Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.000000 Min. :0.000000
1st Qu.:0.000000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.000000 1st Qu.:0.000000
Median :0.000000 Median :0.00000 Median :0.00000 Median :0.00000 Median :0.000000 Median :0.000000
Mean :0.003755 Mean :0.02283 Mean :0.02489 Mean :0.01826 Mean :0.006345 Mean :0.002201
3rd Qu.:0.000000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.000000 3rd Qu.:0.000000
Max. :4.000000 Max. :4.00000 Max. :8.00000 Max. :8.00000 Max. :3.000000 Max. :2.000000
sum_event1_11 sum_event2_1 sum_event2_2 sum_event2_3 sum_event2_4 sum_event2_5
Min. :0.00000 Min. : 0.0000 Min. :0.00000 Min. : 0.0000 Min. : 0.000 Min. :0.00000
1st Qu.:0.00000 1st Qu.: 0.0000 1st Qu.:0.00000 1st Qu.: 0.0000 1st Qu.: 0.000 1st Qu.:0.00000
Median :0.00000 Median : 0.0000 Median :0.00000 Median : 0.0000 Median : 0.000 Median :0.00000
Mean :0.01613 Mean : 0.1134 Mean :0.02092 Mean : 0.2485 Mean : 0.202 Mean :0.06925
3rd Qu.:0.00000 3rd Qu.: 0.0000 3rd Qu.:0.00000 3rd Qu.: 0.0000 3rd Qu.: 0.000 3rd Qu.:0.00000
Max. :7.00000 Max. :10.0000 Max. :5.00000 Max. :14.0000 Max. :14.000 Max. :7.00000
sum_event2_6 sum_event2_7 sum_event2_8 sum_event2_9 sum_event2_10 avg_date_diff
Min. :0.00000 Min. : 0.0000 Min. : 0.0000 Min. : 0.0000 Min. :0.000000 Min. : 0.00
1st Qu.:0.00000 1st Qu.: 0.0000 1st Qu.: 0.0000 1st Qu.: 0.0000 1st Qu.:0.000000 1st Qu.: 75.36
Median :0.00000 Median : 0.0000 Median : 0.0000 Median : 0.0000 Median :0.000000 Median : 204.83
Mean :0.04667 Mean : 0.5932 Mean : 0.2288 Mean : 0.0656 Mean :0.006212 Mean : 254.28
3rd Qu.:0.00000 3rd Qu.: 1.0000 3rd Qu.: 0.0000 3rd Qu.: 0.0000 3rd Qu.:0.000000 3rd Qu.: 390.34
Max. :8.00000 Max. :23.0000 Max. :15.0000 Max. :14.0000 Max. :6.000000 Max. :1095.07
NA's :29613
cumrev_per_prod_till_prev_order rev_per_prod_prev_ord order_month order_week_of_year order_qtr order_day_of_week
Min. : 0.00 Min. : 0.00 01 :18526 01 : 5089 1:46963 Fri:15476
1st Qu.: 0.00 1st Qu.: 0.00 05 :16640 48 : 5053 2:46829 Mon:25323
Median : 0.00 Median : 0.00 12 :16408 49 : 4751 3:45956 Sat:24936
Mean : 33.41 Mean : 33.47 03 :16101 09 : 4591 4:39756 Sun:41578
3rd Qu.: 72.40 3rd Qu.: 67.78 09 :15724 47 : 4414 Thu:21252
Max. :149.98 Max. :150.00 06 :15556 36 : 4387 Tue:23498
(Other):80549 (Other):151219 Wed:27441
order_hour_of_day
19 : 14212
18 : 13804
20 : 12312
17 : 11324
12 : 10465
13 : 10457
(Other):106930 3. Feature Selection
Lets look at the correlation between cumrev_per_prod_till_prev_order and rev_per_prod_prev_ord.
cor(df[,!names(df) %in% c("custno","ordno","orderdate","prodcat1","order_month","order_day_of_week","order_week_of_year","order_qtr","order_hour_of_day")])
num_days_till_last_order sum_category_1 sum_category_2 sum_category_3 sum_event1_1
num_days_till_last_order 1 NA NA NA NA
sum_category_1 NA 1.00000000 0.05975836 0.05260110 0.11519467
sum_category_2 NA 0.05975836 1.00000000 0.07901509 0.22927557
sum_category_3 NA 0.05260110 0.07901509 1.00000000 0.30293379
sum_event1_1 NA 0.11519467 0.22927557 0.30293379 1.00000000
sum_event1_2 NA 0.05190649 0.09216206 0.28816102 0.01454894
sum_event1_4 NA 0.10420820 0.09576677 0.23244340 0.01704493
sum_event1_5 NA 0.03355437 0.18529400 0.08942683 0.04491075
sum_event1_6 NA 0.05581213 0.15496074 0.19627540 0.11837647
sum_event1_7 NA 0.07045872 0.23373840 0.18079784 0.09322193
sum_event1_8 NA 0.03299169 0.12766962 0.09466138 0.03762944
sum_event1_9 NA 0.06742637 0.15114544 0.06032940 0.02045415
sum_event1_10 NA 0.02922822 0.02385869 0.09058968 0.03318439
sum_event1_11 NA 0.05451642 0.14847478 0.18215765 0.01259576
sum_event2_1 NA 0.16400344 0.39534755 0.36162396 0.32771739
sum_event2_2 NA 0.04884802 0.29485586 0.08132352 0.16819145
sum_event2_3 NA 0.14995912 0.28656827 0.69703151 0.19241359
sum_event2_4 NA 0.15237110 0.34116828 0.57082973 0.21609841
sum_event2_5 NA 0.10477098 0.28599343 0.32745477 0.13628671
sum_event2_6 NA 0.04255567 0.15267308 0.34292059 0.06951080
sum_event2_7 NA 0.21068381 0.37149552 0.79573575 0.37683835
sum_event2_8 NA 0.18515614 0.25965403 0.63490593 0.17223948
sum_event2_9 NA 0.11550660 0.19156168 0.38873940 0.15633985
sum_event2_10 NA 0.05779337 0.14661643 0.10350555 0.01087952
avg_date_diff NA NA NA NA NA
cumrev_per_prod_till_prev_order NA 0.03737429 0.09659084 0.10296331 0.08923517
rev_per_prod_prev_ord NA 0.03192756 0.08114139 0.09057785 0.07746783
sum_event1_2 sum_event1_4 sum_event1_5 sum_event1_6 sum_event1_7 sum_event1_8
num_days_till_last_order NA NA NA NA NA NA
sum_category_1 0.051906492 0.104208203 0.033554375 0.055812133 0.070458724 0.032991685
sum_category_2 0.092162057 0.095766765 0.185293999 0.154960744 0.233738403 0.127669616
sum_category_3 0.288161024 0.232443398 0.089426830 0.196275401 0.180797837 0.094661384
sum_event1_1 0.014548941 0.017044927 0.044910752 0.118376472 0.093221932 0.037629442
sum_event1_2 1.000000000 0.106593784 0.009136500 0.043475175 0.005957926 0.021141806
sum_event1_4 0.106593784 1.000000000 0.008942886 0.045010854 0.022378707 0.016567662
sum_event1_5 0.009136500 0.008942886 1.000000000 0.017995510 0.036413875 0.034946981
sum_event1_6 0.043475175 0.045010854 0.017995510 1.000000000 0.039636173 0.041811518
sum_event1_7 0.005957926 0.022378707 0.036413875 0.039636173 1.000000000 0.031112866
sum_event1_8 0.021141806 0.016567662 0.034946981 0.041811518 0.031112866 1.000000000
sum_event1_9 0.003642405 0.012833633 0.196932767 0.014583815 0.015925018 0.014960042
sum_event1_10 0.009662797 0.038373035 0.023348874 0.016737109 0.049604709 0.008740903
sum_event1_11 0.047494832 0.042077314 0.076340648 0.025817024 0.019213420 0.018179601
sum_event2_1 0.126342528 0.078807816 0.096687948 0.138671178 0.147040927 0.067910687
sum_event2_2 0.022814858 0.032483246 0.085843617 0.057584136 0.072103152 0.027882213
sum_event2_3 0.193812238 0.171011851 0.089392936 0.144491018 0.143533072 0.097118603
sum_event2_4 0.180511178 0.087272039 0.105170291 0.125912701 0.163673961 0.116403423
sum_event2_5 0.101470000 0.083240478 0.041504383 0.083644601 0.150389508 0.037910115
sum_event2_6 0.067632969 0.068699315 0.033706739 0.049668450 0.034505390 0.033354643
sum_event2_7 0.327082131 0.326789177 0.158035173 0.264960597 0.270992280 0.116866673
sum_event2_8 0.140534211 0.128928045 0.072376612 0.122953320 0.131704969 0.098336034
sum_event2_9 0.093674460 0.053667104 0.034756614 0.087029808 0.106293839 0.054326345
sum_event2_10 0.017897243 0.007294684 0.176119546 0.009332018 0.017093671 0.022601455
avg_date_diff NA NA NA NA NA NA
cumrev_per_prod_till_prev_order 0.010570714 0.017304208 0.035784992 0.022992106 0.048528785 0.013275841
rev_per_prod_prev_ord 0.007987318 0.015210939 0.030221063 0.019222640 0.039821325 0.009511783
sum_event1_9 sum_event1_10 sum_event1_11 sum_event2_1 sum_event2_2 sum_event2_3
num_days_till_last_order NA NA NA NA NA NA
sum_category_1 0.067426374 0.029228220 0.05451642 0.16400344 0.04884802 0.14995912
sum_category_2 0.151145437 0.023858692 0.14847478 0.39534755 0.29485586 0.28656827
sum_category_3 0.060329405 0.090589681 0.18215765 0.36162396 0.08132352 0.69703151
sum_event1_1 0.020454153 0.033184391 0.01259576 0.32771739 0.16819145 0.19241359
sum_event1_2 0.003642405 0.009662797 0.04749483 0.12634253 0.02281486 0.19381224
sum_event1_4 0.012833633 0.038373035 0.04207731 0.07880782 0.03248325 0.17101185
sum_event1_5 0.196932767 0.023348874 0.07634065 0.09668795 0.08584362 0.08939294
sum_event1_6 0.014583815 0.016737109 0.02581702 0.13867118 0.05758414 0.14449102
sum_event1_7 0.015925018 0.049604709 0.01921342 0.14704093 0.07210315 0.14353307
sum_event1_8 0.014960042 0.008740903 0.01817960 0.06791069 0.02788221 0.09711860
sum_event1_9 1.000000000 0.004387925 0.02605872 0.09968675 0.14183254 0.07038604
sum_event1_10 0.004387925 1.000000000 0.02053569 0.03751542 0.05636781 0.06519097
sum_event1_11 0.026058724 0.020535692 1.00000000 0.07193240 0.01081409 0.11819904
sum_event2_1 0.099686753 0.037515416 0.07193240 1.00000000 0.16491709 0.26790031
sum_event2_2 0.141832536 0.056367806 0.01081409 0.16491709 1.00000000 0.08511606
sum_event2_3 0.070386038 0.065190966 0.11819904 0.26790031 0.08511606 1.00000000
sum_event2_4 0.061545179 0.043629189 0.11121592 0.24067090 0.07451285 0.38841942
sum_event2_5 0.056381737 0.025509788 0.04451130 0.33921453 0.14850369 0.22180114
sum_event2_6 0.046663616 0.015732748 0.06082702 0.20138925 0.10505722 0.23357347
sum_event2_7 0.104482673 0.099699785 0.26412166 0.29528358 0.08976346 0.55632798
sum_event2_8 0.067028737 0.051424380 0.11974492 0.23102153 0.08022814 0.43606937
sum_event2_9 0.042963772 0.033770146 0.04548187 0.15307721 0.06487092 0.21722918
sum_event2_10 0.071174611 0.004239591 0.45808392 0.06973166 0.01221502 0.09121469
avg_date_diff NA NA NA NA NA NA
cumrev_per_prod_till_prev_order 0.031206540 0.008508288 0.01007391 0.09227581 0.04056525 0.08875024
rev_per_prod_prev_ord 0.027600647 0.007865215 0.01005484 0.07749117 0.03459262 0.07729935
sum_event2_4 sum_event2_5 sum_event2_6 sum_event2_7 sum_event2_8 sum_event2_9
num_days_till_last_order NA NA NA NA NA NA
sum_category_1 0.15237110 0.10477098 0.04255567 0.21068381 0.18515614 0.11550660
sum_category_2 0.34116828 0.28599343 0.15267308 0.37149552 0.25965403 0.19156168
sum_category_3 0.57082973 0.32745477 0.34292059 0.79573575 0.63490593 0.38873940
sum_event1_1 0.21609841 0.13628671 0.06951080 0.37683835 0.17223948 0.15633985
sum_event1_2 0.18051118 0.10147000 0.06763297 0.32708213 0.14053421 0.09367446
sum_event1_4 0.08727204 0.08324048 0.06869931 0.32678918 0.12892804 0.05366710
sum_event1_5 0.10517029 0.04150438 0.03370674 0.15803517 0.07237661 0.03475661
sum_event1_6 0.12591270 0.08364460 0.04966845 0.26496060 0.12295332 0.08702981
sum_event1_7 0.16367396 0.15038951 0.03450539 0.27099228 0.13170497 0.10629384
sum_event1_8 0.11640342 0.03791011 0.03335464 0.11686667 0.09833603 0.05432635
sum_event1_9 0.06154518 0.05638174 0.04666362 0.10448267 0.06702874 0.04296377
sum_event1_10 0.04362919 0.02550979 0.01573275 0.09969979 0.05142438 0.03377015
sum_event1_11 0.11121592 0.04451130 0.06082702 0.26412166 0.11974492 0.04548187
sum_event2_1 0.24067090 0.33921453 0.20138925 0.29528358 0.23102153 0.15307721
sum_event2_2 0.07451285 0.14850369 0.10505722 0.08976346 0.08022814 0.06487092
sum_event2_3 0.38841942 0.22180114 0.23357347 0.55632798 0.43606937 0.21722918
sum_event2_4 1.00000000 0.17797305 0.12239740 0.47066984 0.36524952 0.30811130
sum_event2_5 0.17797305 1.00000000 0.27849308 0.22327941 0.19044655 0.11103355
sum_event2_6 0.12239740 0.27849308 1.00000000 0.20742510 0.18095639 0.07453614
sum_event2_7 0.47066984 0.22327941 0.20742510 1.00000000 0.49205418 0.30352810
sum_event2_8 0.36524952 0.19044655 0.18095639 0.49205418 1.00000000 0.25329970
sum_event2_9 0.30811130 0.11103355 0.07453614 0.30352810 0.25329970 1.00000000
sum_event2_10 0.09254652 0.02866873 0.02601103 0.12694000 0.07973688 0.02847559
avg_date_diff NA NA NA NA NA NA
cumrev_per_prod_till_prev_order 0.09585444 0.06096073 0.01976141 0.10435709 0.07829894 0.11248283
rev_per_prod_prev_ord 0.08400979 0.05189747 0.01556599 0.09129023 0.06764350 0.09764213
sum_event2_10 avg_date_diff cumrev_per_prod_till_prev_order rev_per_prod_prev_ord
num_days_till_last_order NA NA NA NA
sum_category_1 0.057793373 NA 0.037374286 0.031927560
sum_category_2 0.146616429 NA 0.096590835 0.081141387
sum_category_3 0.103505548 NA 0.102963309 0.090577852
sum_event1_1 0.010879520 NA 0.089235169 0.077467828
sum_event1_2 0.017897243 NA 0.010570714 0.007987318
sum_event1_4 0.007294684 NA 0.017304208 0.015210939
sum_event1_5 0.176119546 NA 0.035784992 0.030221063
sum_event1_6 0.009332018 NA 0.022992106 0.019222640
sum_event1_7 0.017093671 NA 0.048528785 0.039821325
sum_event1_8 0.022601455 NA 0.013275841 0.009511783
sum_event1_9 0.071174611 NA 0.031206540 0.027600647
sum_event1_10 0.004239591 NA 0.008508288 0.007865215
sum_event1_11 0.458083923 NA 0.010073913 0.010054840
sum_event2_1 0.069731659 NA 0.092275805 0.077491173
sum_event2_2 0.012215024 NA 0.040565252 0.034592618
sum_event2_3 0.091214686 NA 0.088750244 0.077299347
sum_event2_4 0.092546519 NA 0.095854445 0.084009789
sum_event2_5 0.028668733 NA 0.060960725 0.051897473
sum_event2_6 0.026011026 NA 0.019761409 0.015565994
sum_event2_7 0.126940002 NA 0.104357094 0.091290228
sum_event2_8 0.079736877 NA 0.078298936 0.067643502
sum_event2_9 0.028475585 NA 0.112482827 0.097642128
sum_event2_10 1.000000000 NA 0.015234987 0.014600962
avg_date_diff NA 1 NA NA
cumrev_per_prod_till_prev_order 0.015234987 NA 1.000000000 0.880044013
rev_per_prod_prev_ord 0.014600962 NA 0.880044013 1.000000000This is a very high correlation.
cor(df$rev_per_prod_prev_ord,df$cumrev_per_prod_till_prev_order)
[1] 0.880044Therefore, we will choose only one metric as a predictor, which is rev_per_prod_prev_ord.
df$cumrev_per_prod_till_prev_order <- NULLFor categorical variables, we will perform the chi-square test of association. We will compare various columns derived from orderdate.
#"custno","ordno","orderdate","prodcat1","order_month","order_day_of_week","order_week_of_year","order_qtr","order_hour_of_day"
chisq.test(df$order_month,df$order_qtr)
Pearson's Chi-squared test
data: df$order_month and df$order_qtr
X-squared = 538510, df = 33, p-value < 2.2e-16chisq.test(df$order_day_of_week,df$order_hour_of_day)
Pearson's Chi-squared test
data: df$order_day_of_week and df$order_hour_of_day
X-squared = 2343.5, df = 138, p-value < 2.2e-16chisq.test(df$order_day_of_week,df$order_week_of_year)
Pearson's Chi-squared test
data: df$order_day_of_week and df$order_week_of_year
X-squared = 13783, df = 318, p-value < 2.2e-16since the p-value is < 2.2e-16 is less than the cut-off value of 0.05, we can reject the null hypothesis in favor of alternative hypothesis and conclude, that the variables are dependent to each other. Therefore, we will only consider one variable for moedeling, which is order_month and delete the rest.
df[,c("order_day_of_week","order_week_of_year","order_qtr","order_hour_of_day")]<-NULLWe have removed combination of highly correlated variables and highly associated variable. During the model building phase we will encounter some variables that are not significant predictors to the response variable. In those steps, we will still be performing feature selection by removing insignificant predictors and keeping significant ones.
4. Model Designing and sampling
We have prepared the data that now we can use to fit a model. We are trying to fit a model which predicts what product category-1 is a user most likely to buy based on his past online-activity as well as his buying behaviour. We will split the data into training and test sample. We will use the training sample to fit different classification models and test sample to measure the performance of the model. The train-test split is 70-30 split, i.e., 70% of the data is used for training and 30% for testing.
## 70% of the sample size
smp_size <- floor(0.70 * nrow(df))
## set the seed to make your partition reproducible
set.seed(1234)
train_ind <- sample(seq_len(nrow(df)), size = smp_size)
train <- df[train_ind, ]
test <- df[-train_ind, ]Our response mode is prodcat1. We need to make sure that all the classes of prodcat1 are present in train and test samples
table(train$prodcat1)
1 2 3 4 5 7
20958 37549 25483 19725 6735 15202 table(test$prodcat1)
1 2 3 4 5 7
8917 15961 11055 8463 2989 6467 In the next section, we will use different modelling techniques to fit a multi-class classifcation models. We will use the following algorithms 1. Logistic regression 2. Random Forest Regression
Logistic regression works well for linear relationships and has high interpretability, whereas Random Forest can fit non-linear relationships at the cost of interpretation.
The metric we will use to determine the best model is test-AUC (Area under the curve of the ROC curve for test sample)
5. Model Generation and Evaluation
gc()
used (Mb) gc trigger (Mb) max used (Mb)
Ncells 4653526 248.6 8120335 433.7 8120335 433.7
Vcells 133346695 1017.4 1011796314 7719.4 1264734433 9649.2In this step we will fit different models on the training sample and predict for the test sample
Logistic Regrssion
We will fit a mutinomial logistic regression model. We will ignore num_days_till_last_order and avg_date_diff in logistic regression as they have NA values. We could impute those values but given the time constraint, we will choose to ignore them.
summary(glm)
Call:
nnet::multinom(formula = prodcat1 ~ ., data = train1)
Coefficients:
(Intercept) sum_category_1 sum_category_2 sum_category_3 sum_event1_1 sum_event1_2 sum_event1_4 sum_event1_5
2 0.92685719 -0.25976008 -0.21846016 -0.15653215 -0.08278422 -0.008287228 0.08589900 0.3483203
3 -0.01608086 0.55858920 0.59798482 0.52497554 0.20562568 0.007877831 -0.02182606 0.5742525
4 0.09354858 -0.14542476 -0.23535552 -0.01287877 -0.35066917 0.039188349 0.14924121 -0.2160810
5 -0.09783563 0.03098618 0.01213515 0.14495016 -0.03894853 -0.012121087 0.15994628 0.1169564
7 -0.47879203 0.10261985 0.12321927 0.05740280 0.22817106 0.018129963 0.02396771 0.3739307
sum_event1_6 sum_event1_7 sum_event1_8 sum_event1_9 sum_event1_10 sum_event1_11 sum_event2_1 sum_event2_2
2 0.07178375 0.16623964 0.1702947 0.02029412 0.20154455 0.29036966 0.265228758 0.03010450
3 0.09367701 0.02787943 0.5000148 0.47598324 0.27961129 -0.06743240 -0.457797817 -0.46889749
4 -0.01427105 -0.05842807 0.3526541 0.26509099 -0.39961027 0.08591697 0.210933364 -0.33883230
5 -0.03531872 0.01817052 0.5071345 0.67521085 -0.03899443 0.06919961 -0.031773671 -0.13686801
7 0.09535578 -0.05755044 0.3329135 0.35575033 0.15869189 -0.07209661 0.004402445 -0.08104179
sum_event2_3 sum_event2_4 sum_event2_5 sum_event2_6 sum_event2_7 sum_event2_8 sum_event2_9 sum_event2_10
2 -0.19965515 0.16281669 0.23054718 0.18446050 0.12066793 0.23223625 0.26787968 0.158417789
3 -0.59725872 -0.49968157 -0.51793239 -0.47668799 -0.57219192 -0.44079642 -0.40219788 -0.564197358
4 0.17676008 -0.07520873 0.30360473 0.68110953 0.07898073 0.13992636 -0.17966297 0.002290715
5 -0.05680272 -0.15363637 -0.01972262 0.14761678 -0.14574022 0.03230797 -0.07199110 -0.597848602
7 -0.13424732 -0.05260009 -0.04518582 -0.05837584 -0.10786851 0.04617076 0.09463892 -0.265430886
rev_per_prod_prev_ord order_month02 order_month03 order_month04 order_month05 order_month06 order_month07
2 0.0053273175 0.06670542 -0.45679105 -0.6132285 -0.37591534 -0.1397130 0.15680028
3 0.0071552592 0.28015000 -0.02144347 -0.4644083 -0.02060058 0.3571499 0.53346173
4 0.0032106312 -0.15238535 -0.06834588 -0.7880644 -0.52247659 0.3878547 0.08487551
5 0.0009114869 -1.19706345 -2.29136974 -3.0809798 -2.83136757 -2.2205060 -1.96490684
7 0.0048534076 0.12131887 -0.15204343 -0.4647843 -0.06303049 0.2404515 0.31380264
order_month08 order_month09 order_month10 order_month11 order_month12
2 0.08873367 -0.05275182 -0.86105906 -1.6318948 -1.22583565
3 0.52023102 0.27756253 -0.39333021 -1.1316142 -0.63581421
4 -0.02500962 0.27402639 -0.92151454 -1.6003521 -1.05343164
5 -1.50390169 -2.04718750 -0.92900361 -0.9209117 -0.11145054
7 0.35897002 0.11152224 -0.06629529 -0.4029704 -0.03868497
Std. Errors:
(Intercept) sum_category_1 sum_category_2 sum_category_3 sum_event1_1 sum_event1_2 sum_event1_4 sum_event1_5
2 0.02945365 0.17988685 0.17922265 0.17902124 0.03476902 0.04343567 0.04584102 0.1786825
3 0.03393588 0.03838143 0.03580656 0.03552862 0.03130057 0.04323451 0.04819045 0.1654328
4 0.03353468 0.09035515 0.08901041 0.08852505 0.04016560 0.04235464 0.04569478 0.2270410
5 0.03582922 0.03272326 0.02350971 0.02113128 0.04332606 0.05688463 0.05848935 0.2592145
7 0.03878963 0.04114675 0.03837509 0.03808549 0.03365701 0.04832331 0.05311936 0.1847943
sum_event1_6 sum_event1_7 sum_event1_8 sum_event1_9 sum_event1_10 sum_event1_11 sum_event2_1 sum_event2_2
2 0.06164166 0.05155020 0.07101928 0.1366665 0.1949923 0.06984685 0.18072836 0.18900791
3 0.06104808 0.05080723 0.06691153 0.1229846 0.1916470 0.07820674 0.04422801 0.06451373
4 0.06646928 0.05944062 0.07303186 0.1446586 0.2266176 0.07769831 0.09302578 0.11676610
5 0.09005482 0.07406142 0.08587598 0.1685918 0.3068402 0.11487523 0.04243847 0.09207128
7 0.06780314 0.05758238 0.07535617 0.1364164 0.2244613 0.09060666 0.04783762 0.07171956
sum_event2_3 sum_event2_4 sum_event2_5 sum_event2_6 sum_event2_7 sum_event2_8 sum_event2_9 sum_event2_10
2 0.18014630 0.18014371 0.18180052 0.18463314 0.17925412 0.17959376 0.18214907 0.2094330
3 0.03974465 0.04044870 0.04928406 0.05686271 0.03731785 0.04041361 0.04874715 0.1178595
4 0.09038571 0.09104484 0.09507335 0.09726251 0.08934447 0.09055962 0.09726662 0.1503641
5 0.03185839 0.03446989 0.05159846 0.05848379 0.02674471 0.03299538 0.05096873 0.1970621
7 0.04298014 0.04384333 0.05366494 0.06322264 0.04013347 0.04360766 0.05263676 0.1395643
rev_per_prod_prev_ord order_month02 order_month03 order_month04 order_month05 order_month06 order_month07
2 0.0002169191 0.04530423 0.04083369 0.03930674 0.03960859 0.04359164 0.04377803
3 0.0002276530 0.05078367 0.04551531 0.04568981 0.04462479 0.04782732 0.04815532
4 0.0002525343 0.05303935 0.04543052 0.04728159 0.04688303 0.04730412 0.04997951
5 0.0003425137 0.07165402 0.08381117 0.10439219 0.09946907 0.09460615 0.08901990
7 0.0002559565 0.05893696 0.05309151 0.05305669 0.05139468 0.05493363 0.05560687
order_month08 order_month09 order_month10 order_month11 order_month12
2 0.04450789 0.04296455 0.05119891 0.04178776 0.04281439
3 0.04870952 0.04775199 0.05518960 0.04628534 0.04657055
4 0.05126673 0.04738420 0.06209392 0.05085691 0.04976748
5 0.07707928 0.08703584 0.06894489 0.04962812 0.04784662
7 0.05584312 0.05537830 0.06084246 0.04930314 0.05038297
Residual Deviance: 402777.3
AIC: 403137.3 Now we’ll calculate Z score and p-Value for the variables in the model.
z <- summary(glm)$coefficients/summary(glm)$standard.errorsCalculating the the odds ratio coefficient for each predictor
exp(coef(glm)) (Intercept) sum_category_1 sum_category_2 sum_category_3 sum_event1_1 sum_event1_2 sum_event1_4 sum_event1_5
2 2.5265562 0.7712366 0.8037555 0.8551040 0.9205498 0.9917470 1.0896963 1.4166860
3 0.9840478 1.7482044 1.8184506 1.6904175 1.2282933 1.0079089 0.9784104 1.7758026
4 1.0980639 0.8646549 0.7902898 0.9872038 0.7042167 1.0399663 1.1609530 0.8056701
5 0.9067979 1.0314713 1.0122091 1.1559820 0.9618002 0.9879521 1.1734478 1.1240704
7 0.6195313 1.1080701 1.1311324 1.0590823 1.2563002 1.0182953 1.0242572 1.4534364
sum_event1_6 sum_event1_7 sum_event1_8 sum_event1_9 sum_event1_10 sum_event1_11 sum_event2_1 sum_event2_2
2 1.0744230 1.1808560 1.185654 1.020501 1.2232907 1.3369216 1.3037292 1.0305622
3 1.0982050 1.0282717 1.648746 1.609596 1.3226156 0.9347909 0.6326754 0.6256917
4 0.9858303 0.9432461 1.422839 1.303550 0.6705813 1.0897158 1.2348301 0.7126019
5 0.9652977 1.0183366 1.660526 1.964447 0.9617561 1.0716501 0.9687258 0.8720853
7 1.1000502 0.9440743 1.395027 1.427251 1.1719768 0.9304410 1.0044122 0.9221552
sum_event2_3 sum_event2_4 sum_event2_5 sum_event2_6 sum_event2_7 sum_event2_8 sum_event2_9 sum_event2_10
2 0.8190131 1.1768210 1.2592889 1.2025695 1.1282502 1.2614177 1.3071898 1.1716556
3 0.5503181 0.6067238 0.5957511 0.6208362 0.5642872 0.6435237 0.6688484 0.5688165
4 1.1933447 0.9275499 1.3547335 1.9760690 1.0821835 1.1501891 0.8355518 1.0022933
5 0.9447804 0.8575838 0.9804706 1.1590686 0.8643822 1.0328355 0.9305392 0.5499936
7 0.8743738 0.9487594 0.9558199 0.9432954 0.8977456 1.0472532 1.0992619 0.7668754
rev_per_prod_prev_ord order_month02 order_month03 order_month04 order_month05 order_month06 order_month07
2 1.005342 1.0689805 0.6333127 0.54159947 0.6866605 0.8696078 1.1697620
3 1.007181 1.3233283 0.9787848 0.62850687 0.9796102 1.4292500 1.7048237
4 1.003216 0.8586573 0.9339374 0.45472411 0.5930500 1.4738156 1.0885815
5 1.000912 0.3020800 0.1011278 0.04591425 0.0589322 0.1085542 0.1401689
7 1.004865 1.1289849 0.8589510 0.62827063 0.9389148 1.2718232 1.3686196
order_month08 order_month09 order_month10 order_month11 order_month12
2 1.0927896 0.9486154 0.4227142 0.1955587 0.2935123
3 1.6824163 1.3199086 0.6748059 0.3225122 0.5295042
4 0.9753005 1.3152495 0.3979159 0.2018254 0.3487389
5 0.2222613 0.1290975 0.3949470 0.3981559 0.8945356
7 1.4318539 1.1179786 0.9358545 0.6683319 0.9620537Calculate Variable importance (absolute value of t-statistic)
varimp_glm %>% arrange(desc(importance))
importance predictor
1 5.68774320 order_month11
2 5.41146528 order_month04
3 3.81339058 order_month05
4 3.34567502 order_month06
5 3.17120271 order_month10
6 3.06521701 order_month12
7 3.05384700 order_month07
8 2.98999357 order_month03
9 2.76305048 order_month09
10 2.49684603 order_month08
11 1.86301165 sum_event1_8
12 1.81762310 order_month02
13 1.79232953 sum_event1_9
14 1.62954085 sum_event1_5
15 1.58818535 sum_event2_10
16 1.54825064 sum_event2_6
17 1.18715492 sum_category_2
18 1.16472398 sum_event2_3
19 1.11699275 sum_event2_5
20 1.09738007 sum_category_1
21 1.07845244 sum_event1_10
22 1.05574408 sum_event2_2
23 1.02544930 sum_event2_7
24 1.01637055 sum_event2_9
25 0.97013605 sum_event2_1
26 0.94394345 sum_event2_4
27 0.90619866 sum_event1_1
28 0.89673941 sum_category_3
29 0.89143776 sum_event2_8
30 0.58501525 sum_event1_11
31 0.44088025 sum_event1_4
32 0.32826810 sum_event1_7
33 0.31040629 sum_event1_6
34 0.08560446 sum_event1_2
35 0.02145810 rev_per_prod_prev_ordWe can see that order month is the most important parameter. This is evident from the time series trends that we observed while exploring the data. Other important variables were sum_event1_8 ,sum_event1_8, and sum_event1_5
Let’s check for fitted values now.
head(fitted(glm))
1 2 3 4 5 7
1 0.1362019 0.3347793 0.1507843 0.14873830 0.13157759 0.09791863
2 0.2078132 0.2037986 0.1576077 0.09417795 0.17682666 0.15977590
3 0.1982757 0.2971629 0.1782158 0.21250755 0.01799667 0.09584135
4 0.1406811 0.3090922 0.1978609 0.22767029 0.01384818 0.11084742
5 0.1918412 0.3069652 0.1847759 0.19673760 0.01759233 0.10208775
6 0.1406811 0.3090922 0.1978609 0.22767029 0.01384818 0.11084742predicting on the test data
predict_tst=as.data.frame(predict(glm,test1,type="probs"))
colnames(predict_tst)<-sapply(colnames(predict_tst), function(x) paste('logit_',x,sep = ""))
predict_tst$predicted_class<-apply(predict_tst,1,which.max)
predict_tst$predicted_class<-ifelse(predict_tst$predicted_class==6,7,predict_tst$predicted_class)
head(predict_tst)
logit_1 logit_2 logit_3 logit_4 logit_5 logit_7 predicted_class
1 0.1406811 0.3090922 0.1978609 0.22767029 0.01384818 0.1108474 2
2 0.3020623 0.1545535 0.1508060 0.09982670 0.12735199 0.1653995 1
3 0.1137407 0.2836578 0.3157333 0.12195955 0.01317366 0.1517349 3
4 0.1918412 0.3069652 0.1847759 0.19673760 0.01759233 0.1020877 2
5 0.1550755 0.2313376 0.2066006 0.09049224 0.14177102 0.1747231 2
6 0.1305176 0.3721515 0.2088617 0.16667300 0.01657632 0.1052199 2Creating confusion matrix for test sample
tab<-table(predict_tst$predicted_class,test1$prodcat1)
library(caret)
conf<-confusionMatrix(tab)
confConfusion Matrix and Statistics
1 2 3 4 5 7
1 1744 1091 1018 617 919 1090
2 6219 13703 8312 6233 1550 4407
3 489 607 1155 326 176 590
4 336 446 419 1167 146 246
5 108 91 118 114 183 113
7 21 23 33 6 15 21
Overall Statistics
Accuracy : 0.3337
95% CI : (0.3298, 0.3377)
No Information Rate : 0.2964
P-Value [Acc > NIR] : < 2.2e-16
Kappa : 0.0945
Mcnemar's Test P-Value : < 2.2e-16
Statistics by Class:
Class: 1 Class: 2 Class: 3 Class: 4 Class: 5 Class: 7
Sensitivity 0.19558 0.8585 0.10448 0.13789 0.061224 0.003247
Specificity 0.89463 0.2948 0.94887 0.96490 0.989305 0.997932
Pos Pred Value 0.26918 0.3390 0.34550 0.42283 0.251719 0.176471
Neg Pred Value 0.84858 0.8318 0.80400 0.85720 0.947181 0.880036
Prevalence 0.16558 0.2964 0.20528 0.15715 0.055504 0.120088
Detection Rate 0.03239 0.2545 0.02145 0.02167 0.003398 0.000390
Detection Prevalence 0.12031 0.7506 0.06208 0.05125 0.013500 0.002210
Balanced Accuracy 0.54510 0.5767 0.52668 0.55140 0.525265 0.500590Class2 has high sensitivity, which means the model has a higher True Positive Rate for Class2. This means that the model does a good job of predicting whether a customer will will buy product category 2. At the same time it does a poor job of predicting whether a customer is not going to buy a product from prodcat2 or not. This is evident from the specificity of Class2
If we we look at the sensitivity and specificity across all the other classes, we will see that the sensitivity values are low and specificity values are high. This means that, for the other classes the model does a better job identifying whether a customer is not going to buy a product in that class than predicting whether a customer is going to buy a product in that class
Calculating Test AUC of the ROC curve. The AUC is a measure of how well a model does a job of distinguishing between classes
library(HandTill2001)
auc(multcap(response=test1$prodcat1,predicted = predict(glm,test1,type="probs")))
[1] 0.652249This is a decent value. But it could be improved further by using complex models.
Random Forest Classification
# train1<- train
# test1<- test
# train1[,c("num_days_till_last_order","avg_date_diff")]<-NULL
# test1[,c("num_days_till_last_order","avg_date_diff")]<-NULL
library(randomForest)
# Fit the model
set.seed(1234)
rf <- randomForest(prodcat1 ~., data = train1, ntree=500, mtry=round(sqrt(ncol(train)-1)), importance=TRUE)
# Summarize the model
rf
Call:
randomForest(formula = prodcat1 ~ ., data = train1, ntree = 500, mtry = round(sqrt(ncol(train) - 1)), importance = TRUE)
Type of random forest: classification
Number of trees: 500
No. of variables tried at each split: 5
OOB estimate of error rate: 66.58%
Confusion matrix:
1 2 3 4 5 7 class.error
1 4842 12678 1414 1321 359 344 0.7689665
2 3180 29391 2379 1889 279 431 0.2172628
3 2710 16849 3334 1560 289 741 0.8691677
4 1882 12550 1175 3672 278 168 0.8138403
5 2048 3063 419 563 472 170 0.9299183
7 2540 9327 1965 815 267 288 0.9810551Calculate Variable importance
varImp(rf) 1 2 3 4 5 7
sum_category_1 -5.1193393 43.557678 -24.368299 -9.375528 -2.3120335 -14.4477247
sum_category_2 5.3160834 67.981092 -18.337293 -11.836191 -0.1298790 -17.6503732
sum_category_3 -0.2800313 56.653897 -39.581179 27.917861 15.0713591 -38.6677828
sum_event1_1 17.1193495 31.637741 -12.529545 -5.440176 -3.7171077 -6.3085222
sum_event1_2 0.7737313 12.986533 -9.571350 -8.408507 0.3338238 -2.8592123
sum_event1_4 -2.0829410 14.300008 -6.252205 -11.700814 6.9362477 -9.8811662
sum_event1_5 4.8315502 9.508437 4.800939 8.999123 10.6495981 -0.5754956
sum_event1_6 6.0840557 17.179022 -14.475398 -7.191722 13.7507759 -8.3775457
sum_event1_7 0.6309928 12.988774 -4.969941 -15.301061 3.5977528 -6.7350553
sum_event1_8 1.6809914 26.299258 -11.317356 -10.896376 15.3511229 -2.5753725
sum_event1_9 3.8090363 15.657352 -1.720984 -2.980269 1.7098612 -8.2161648
sum_event1_10 4.3594627 3.671061 4.854107 -7.998542 0.9822861 -2.0048350
sum_event1_11 5.2903459 13.209633 -2.836639 -11.024353 2.3213302 -4.2730299
sum_event2_1 7.3919165 27.925765 -18.059779 -14.395289 -3.2902597 -18.8961765
sum_event2_2 0.1331095 25.161970 -11.042390 -1.391763 0.3898599 -12.1770148
sum_event2_3 -18.2321937 75.808697 -28.973634 23.285029 15.4449986 -23.8456466
sum_event2_4 2.6477241 28.206531 -14.937120 -35.242783 -6.7149926 -14.6255530
sum_event2_5 4.4391053 27.434754 -18.862426 -4.914085 -3.5118249 -14.1544791
sum_event2_6 3.0745857 41.172743 -17.347414 28.037381 8.6371019 -13.9914822
sum_event2_7 -4.1280749 34.081676 -23.000965 -9.888816 -0.3076361 -25.7277140
sum_event2_8 5.5807164 26.837586 -19.050343 -10.967575 1.9857983 -17.0012923
sum_event2_9 2.5006326 24.550648 -15.510322 -9.932935 4.9804470 -9.4825662
sum_event2_10 6.4064705 8.803003 -5.048304 -7.585508 3.5674212 -3.2029759
rev_per_prod_prev_ord -8.2350514 29.043473 29.737574 38.254197 -2.4392634 2.9193443
order_month 39.6092151 67.915286 17.223029 60.407128 106.0496162 8.1327850Similar to what we have observed in the multinomial logistic regression, we can see that order month is the most important predictor.
predicting on the test data
head(predict_tst_rf)
rf_1 rf_2 rf_3 rf_4 rf_5 rf_7 predicted_class_rf
1 0.000 1.000 0.000 0.000 0.000 0.000 2
2 0.862 0.056 0.020 0.046 0.008 0.008 1
3 0.050 0.298 0.294 0.192 0.016 0.150 2
4 0.002 0.998 0.000 0.000 0.000 0.000 2
5 0.204 0.552 0.064 0.000 0.124 0.056 2
6 0.002 0.998 0.000 0.000 0.000 0.000 2Creating confusion matrix for test sample
tab_rf<-table(predict_tst_rf$predicted_class_rf,test1$prodcat1)
library(caret)
conf_rf<-confusionMatrix(tab_rf)
conf_rfConfusion Matrix and Statistics
1 2 3 4 5 7
1 2014 1402 1189 787 945 1108
2 5430 12475 7323 5457 1323 3934
3 613 1024 1453 501 164 843
4 601 780 644 1538 278 331
5 111 112 132 104 195 117
7 148 168 314 76 84 134
Overall Statistics
Accuracy : 0.3307
95% CI : (0.3267, 0.3347)
No Information Rate : 0.2964
P-Value [Acc > NIR] : < 2.2e-16
Kappa : 0.1037
Mcnemar's Test P-Value : < 2.2e-16
Statistics by Class:
Class: 1 Class: 2 Class: 3 Class: 4 Class: 5 Class: 7
Sensitivity 0.2259 0.7816 0.13143 0.18173 0.065239 0.020721
Specificity 0.8791 0.3807 0.92651 0.94197 0.988675 0.983328
Pos Pred Value 0.2705 0.3471 0.31601 0.36865 0.252918 0.145022
Neg Pred Value 0.8513 0.8054 0.80505 0.86061 0.947363 0.880347
Prevalence 0.1656 0.2964 0.20528 0.15715 0.055504 0.120088
Detection Rate 0.0374 0.2317 0.02698 0.02856 0.003621 0.002488
Detection Prevalence 0.1382 0.6674 0.08538 0.07747 0.014317 0.017158
Balanced Accuracy 0.5525 0.5811 0.52897 0.56185 0.526957 0.502024The accuracy of the model is similar to the multinomial logisitic regression. Even the sensitivity and specificity across the classes is similar to multinomial logistic regression. Class 2 has high sensitivity and low specificity and all the other classes have low sensitivity and high specificity.
Calculating Test AUC of the ROC curve
library(HandTill2001)
auc(multcap(response=test$prodcat1,predicted = predict(rf,test1,type="prob")))
[1] 0.5773988The random forest model has better fit on the training data, as evident from the model summary, but it does not do a job better than multinomial logistic regression to seperate the classes. One possible reason could be that we did not choose that big of an ensemble. The number of trees that we choose in the forest were only 500. If we increase it, the performance will improve.
Random Forest with hyper parameter tuning
We tune the hyperparameters of random forest model so that it can converge on a more optimal output. There are two hyper parameters of the random forest
1. mtry: number of predictors randomly chosen for the decision trees in the forests 2. ntree: total number of decision trees in the forest.
One caveat though, this process requires a lot of computation and takes some time to converge.
levels(train1$prodcat1)<-c("cat1","cat2","cat3","cat4","cat5","cat7")
levels(test1$prodcat1)<-c("cat1","cat2","cat3","cat4","cat5","cat7")library(tidyverse)
library(caret)
library(randomForest)
customRF <- list(type = "Classification", library = "randomForest", loop = NULL)
customRF$parameters <- data.frame(parameter = c("mtry", "ntree"), class = rep("numeric", 2), label = c("mtry", "ntree"))
customRF$grid <- function(x, y, len = NULL, search = "grid") {}
customRF$fit <- function(x, y, wts, param, lev, last, weights, classProbs, ...) {
randomForest(x, y, mtry = param$mtry, ntree=param$ntree, ...)
}
customRF$predict <- function(modelFit, newdata, preProc = NULL, submodels = NULL)
predict(modelFit, newdata)
customRF$prob <- function(modelFit, newdata, preProc = NULL, submodels = NULL)
predict(modelFit, newdata, type = "prob")
customRF$sort <- function(x) x[order(x[,1]),]
customRF$levels <- function(x) x$classescontrol <- trainControl(method="cv", number=10, #repeats=3,
classProbs = TRUE)
tunegrid <- expand.grid(.mtry=c(15:18), .ntree=c(500, 1000))
set.seed(1234)
custom <- train(prodcat1~., data=train1, method=customRF, metric="ROC", tuneGrid=tunegrid, trControl=control)
summary(custom)
plot(custom)I have included the code but has not run it as it takes a lot of time to run and knit the report.
6. Summary
To summarise, we had the customer order data as well as customer online activity data. We explored the data and found out that there is a seasonality in the revenue, number of orders, as well as the online activity. It peaks during Nov and Dec and drops during the months of Feb and Oct. We also saw that this trend is consitent across browsing categories as well as differnet online events. We also found out that most of the online activity is done on browsing category 3.
We also tried associating customer order data with online behaviour. While doing so, we made an assumption
*1. Only the last 30 days of online activity drives buying behaviour for a customer.
Any activity before that does not affect buying behaviour significantly. Based on this assumption, we have merged the online data with the order data. We were also able to derive som metrics like, count of each online event before the purchase, Number of days since last order, order month etc. We have used this metric to predict product category-1.
The predictive problem we are trying to solve is: Based on historical purchases and online beviour, what is the likelihood that a customer would purchase a product from a product-category1. To fit and measure the performance of the model, we first split the data into training and test sample. 70% of the data is used for training and 30% for measure its performance on unseen data. We have tried multinomial logistic regression, random forest, and random forest with hyper parameter tuning. Both the models performed decent on the test data. The models are good at identifying whether a customer is not going to buy from a particular product-category. The AUC value shows that the model does a decent job of separating classes in logistic regression. To improve the performance of the random forest model, we can perform hyperparameter tuning using a grid-search approach. This process takes a lot of time and computation capacity. I have shared the code for doing that.
With a better predicitve power, we can predict with high accuracy the product category where a customer is mostly likely to shop from. We can use this information to run targeted campaign or provide incentive to buy back from us.
---
title: "R Notebook"
output: html_notebook
---

#Data Science Homework - Homework assignment for Data Scientist candidate

#####Loading the needed libraries and setting the working directory

```{r}

library(tidyverse)
library(lubridate)
rm(list=ls())
getwd()
setwd('C:/Users/KPatel/OneDrive - CBRE, Inc/Documents/career/Shutterfly')
```

#####Importing the data from the zip file
```{r}
order <- read.table(unz("data.zip", "order.csv"), header=T, quote="\"", sep=",")
online<- read.table(unz("data.zip", "online.csv"), header=T, quote="\"", sep=",")
```


##1. Exploration and understanding of the data sets

###Order dataset
Lets look at the structure of the data
```{r}
str(order)
```
we can see that the custno, ordno, prodcat2, prodcat1 are integer but should be factors. Also, orderdate is a factor which should be a Datetime column. Changing the data type of these columns.
```{r}
order[c('custno','ordno','prodcat1','prodcat2')] <- lapply(order[c('custno','ordno','prodcat1','prodcat2')], factor)  ## as.factor() could also be used

order$orderdate <- strptime(x = as.character(order$orderdate),
                                format = "%Y-%m-%d %H:%M:%S")
order$orderdate <- as.POSIXct(order$orderdate, tz = "", format="%Y-%m-%d %H:%M:%S")

str(order)
```

Now lets look at the summary of the data.
```{r}
summary(order)
```
We can see that we have the order data for years 2016, 2017, and 2018. We can also see that there are some missing values in prodcat2.

Lets explore at prodcat2
```{r}
length(unique(order$prodcat2))
```
We have 252 levels in the prodcat2 categorical variable. Lets try to understand the mapping between prodcat1 and prodcat2
```{r}
tab<-table(order$prodcat2,order$prodcat1)
head(tab,50)
```
There are also NA's in the prodcat2.
```{r}
summary(order$prodcat2)
```
There are 1823 NA's in the prodcat2 field. We could impute these values using statistical methods. However, given the time-constraint, we won't dive deep into prodcat2.

Lets first understand the level of the data. Intuitively, it looks like that the data is at product level. Lets check that by aggregating data.
```{r}
level_ord<- order %>% group_by(custno,ordno,orderdate,prodcat1,prodcat2) %>% summarise(cnt=n()) %>% arrange(desc(cnt))
head(level_ord)
```

We can see that for custno 9 and ordno 23204, we are getting the cnt of more than 1 for each combination of prodcat1 and prodcat2. Lets look at the order data for this case
```{r}
order %>% filter(custno==9,ordno==23204)
```
We clearly see from the above example that the data is at product level. Lets get it at order and prodcat1 level.
```{r}
order_agg<- order %>% group_by(custno,ordno,orderdate,prodcat1) %>% summarise(revenue = sum(revenue), num_prod = n())
head(order_agg,10)
```



Lets look at revenue.
```{r}
summary(order$revenue)

hist(order$revenue,breaks = 30)
```
We can see from the histogram that revenue is uniformly distributed. Lets check revenue and ordersize across different prodcat1 and customers
```{r}
order %>% group_by(prodcat1) %>% summarise(avg_rev_per_product=mean(revenue),total_rev=sum(revenue),num_orders=length(unique(ordno)),cnt_cust=length(unique(custno)))
```
From the above data we can see that the prodcat1=1 has the highest sales volume both in terms of revenue, number of orders as well as number of customers, whereas prodcat1=5 has the lowest.


Lets look at trend in revenue with time
```{r fig.width=9}
library(lubridate)


order %>% mutate(Year_Month=format(as.Date(orderdate), "%Y-%m")) %>% group_by(Year_Month) %>% summarise(revenue=sum(revenue)) %>% ggplot(aes(x=Year_Month,y=revenue)) + geom_bar(stat='identity')+
xlab('orderdate')+ylab('Revenue')+ theme(axis.text.x = element_text(angle = 90, hjust = 1))#+ggtitle("Cumulative")

```
We can see a seasonlaity here. The Revenue peaks during the months of Dec and Jan. It then drops during the month of Feb and starts rising again and reaches another peak around May-June and then plunges in Oct. Then it rises again and peaks in Dec-Jan. The highest revenue was earned in Jan-2017 and lowest in Oct-2018.Lets break it down across product category and see if we get any seasonality across prodcat1. 

```{r fig.width=15, fig.height=10}
order %>% mutate(Year_Month=format(as.Date(orderdate), "%Y-%m")) %>% group_by(Year_Month,prodcat1) %>% summarise(revenue=sum(revenue)) %>% ggplot(aes(x=Year_Month,y=revenue,color=prodcat1,group=prodcat1)) +                    geom_line()+ facet_wrap(~prodcat1,nrow=3, scales = 'free') +
xlab('orderdate')+ylab('Revenue')+ theme(axis.text.x = element_text(angle = 90, hjust = 1))#+ggtitle("Cumulative")


```
We can see a seasonality across all the prodcat1 similar to the overall revenue category

We expect a similar trend for num_products ordered. Lets calculate the correlation between revenue and number of products ordered.

```{r}
cor(order_agg$revenue,order_agg$num_prod)
```
The two fields are highly correlated which is evident from the scatter-plot given below
```{r}
order_agg %>% ggplot(aes(x=revenue,y=num_prod)) + geom_point()
```

Lets look at the scatterplot across each product category and calculate the correlation at that level.
```{r fig.width=15, fig.height=10}
order_agg %>% ggplot(aes(x=revenue,y=num_prod)) + geom_point()+ facet_wrap(~prodcat1,nrow=3, scales = 'free')
```

```{r}
order_agg %>% group_by(prodcat1) %>% summarise(cor_rev_prod=cor(revenue,num_prod))
```
The correlation across each prodcat1 is high.


###Online dataset
Lets look at the structure of the data
```{r}
str(online)
```

The categorical columns custno, category, event1, event2, session, and visitor are in integer and the dt column should be of datetime datetype.
```{r}
online[c('session','visitor','custno','category','event1','event2')] <- lapply(online[c('session','visitor','custno','category','event1','event2')], factor)  ## as.factor() could also be used

online$dt <- strptime(x = as.character(online$dt),
                                format = "%Y-%m-%d %H:%M:%S")
online$dt <- as.POSIXct(online$dt, tz = "", format="%Y-%m-%d %H:%M:%S")

str(online)
```

Lets look at the summary of the data
```{r}
summary(online)
```
We can see that the duration of the online data is from Jan-2016 to Dec-2017. We have 3 levels in online browsing category and multiple levels in event1 and event2. Lets first compare the number of customers in online vs order.
```{r}
length(unique(online$custno))
length(unique(order$custno))
```
There are 57584 customers in online and 70264 customers in the order dataset. Getting a list of customers common to both the datasets
```{r}
common_cust<-unique(order[which(order$custno %in% unique(online$custno)),]$custno)
length(common_cust)
```
Lets calculate online activity across each of online browsing categories.
```{r}
online %>% group_by(category) %>% summarise(activity=n(),unique_sessions=length(unique(session)),num_cust=length(unique(custno)))
```
Here activity means any sort of activity, be it creation of session, change in event1 or event2 etc. Unique sessions is the count of unique sessions created on each category and new_cust is the number of unique customers that used that category. Here, online browsing category could mean which device or what channel is used by the customer to browse the website.

Moving onto event1, we can see that majority of the values in that field are null
```{r}
prop.table(table(online$event1,useNA = "ifany"))*100
```
83% of the values are null in event1. We will assume here that all the null values in event1 belong to one class which is class 0.
```{r}
levels(online$event1)
online$event1<-factor(ifelse(is.na(online$event1), 0, paste(online$event1)), levels = c(levels(online$event1), 0))
levels(online$event1)
prop.table(table(online$event1))*100
```


Lets look at event2,
```{r}
prop.table(table(online$event2,useNA = "ifany"))*100
```
We can see that event2 is a highly imbalanced class with 39% of the data is in class 7 and 14% in class3. Lets look at online activity across each of the class in event2.
```{r}
online %>% group_by(event2) %>% summarise(activity=n(),unique_sessions=length(unique(session)),num_cust=length(unique(custno)))
```
AS expected, most of the activity is across class7 followed by class3 and class8. However, its still not enough to tell us what the value of each those class means.

Lets look at the time series trends of online activity
```{r fig.width=11, fig.height=4}
online %>% mutate(Year_Month=format(as.Date(dt), "%Y-%m")) %>% group_by(Year_Month) %>% summarise(activity=n(),unique_sessions=length(unique(session)),num_cust=length(unique(custno)))%>% ggplot() + geom_line(aes(x = Year_Month, y = activity, group=1, colour = "activity")) + 
geom_line(aes(x = Year_Month, y = unique_sessions, group=2, colour = "unique_sessions")) + 
geom_line(aes(x = Year_Month, y = num_cust, group=2, colour = "num_cust"))+ theme(axis.text.x = element_text(angle = 90, hjust = 1))
```

We will further break it down by browsing category
```{r fig.width=11, fig.height=6}
online %>% mutate(Year_Month=format(as.Date(dt), "%Y-%m")) %>% group_by(Year_Month,category) %>% summarise(activity=n(),unique_sessions=length(unique(session)),num_cust=length(unique(custno)))%>% ggplot() + geom_line(aes(x = Year_Month, y = activity, group=1, colour = "activity")) + 
geom_line(aes(x = Year_Month, y = unique_sessions, group=2, colour = "unique_sessions")) + 
geom_line(aes(x = Year_Month, y = num_cust, group=2, colour = "num_cust"))+
facet_wrap(~category, nrow=2,scales = 'free') +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
```


Lets break down online activity by event2.
```{r fig.height=15}
online %>% mutate(Year_Month=format(as.Date(dt), "%Y-%m")) %>% group_by(Year_Month,event2) %>% summarise(activity=n(),unique_sessions=length(unique(session)),num_cust=length(unique(custno)))%>% ggplot() + geom_line(aes(x = Year_Month, y = activity, group=1, colour = "activity")) + 
geom_line(aes(x = Year_Month, y = unique_sessions, group=2, colour = "unique_sessions")) + 
geom_line(aes(x = Year_Month, y = num_cust, group=2, colour = "num_cust"))+
facet_wrap(~event2, nrow=5,scales = 'free') +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
```


From all the online activity plot, we can see a seasonality trend. The online activity starts peaking from Nov till Jan then falls to the lowest in Feb. It then remains pretty steady till Oct. This trend is similar to the one we obtained for revenue and number of orders.

##2.Feature engineering
Lets try to understand the level of the data in online dataset.
```{r}
level_online<-online %>% group_by(session,custno,dt,event1,event2)%>% summarise(cnt=n()) %>% arrange(desc(cnt)) 
head(level_online)
```
We can see that each record is uniquely identified at session, customer, datetime, event1, and event2. Lets change the level of the data by spreading the online data on event2
```{r}
online$val<-1
online_spread_e2<-spread(online,event2,val,fill=0,sep = '_')
head(online_spread_e2)
online$val<-NULL
```
We will further spread the online data on key event1.
```{r}
online_spread_e2$val<-1
online_spread_e2e1<-spread(online_spread_e2,event1,val,fill=0,sep = '_')

head(online_spread_e2e1)
```

There is also a possibility that a customer can use different browsing categories (for example, custno 6). To account for that we have to spread the data by category as well.
```{r}
online_spread_e2e1$val<-1
online_spread_e2e1cat<-spread(online_spread_e2e1,category,val,fill=0,sep = '_')

head(online_spread_e2e1cat)
```

Now, we will engineer features from Order data. One set of important features are is the revenue made by a customer on the last order of the same product category as well as and the number number of items ordered the last time. I have created those features below

```{r}

order_agg<- order_agg %>% arrange(custno,prodcat1,orderdate,) %>% group_by(custno, prodcat1) %>% mutate(cum_rev=cumsum(revenue), cum_num_prod=cumsum(num_prod))


order_agg$cumrev_till_prev_order <- order_agg$cum_rev - order_agg$revenue
order_agg$cumnum_prod_till_prev_order <- order_agg$cum_num_prod - order_agg$num_prod
order_agg <- order_agg %>% arrange(custno,prodcat1,orderdate) %>%
  group_by(custno,prodcat1) %>%
  mutate(rev_prev_ord = dplyr::lag(revenue, n = 1, default = 0),num_prod_prev_ord = dplyr::lag(num_prod, n = 1, default = 0))

order_agg[,c("revenue","num_prod","cum_rev","cum_num_prod")]<-NULL
summary(order_agg)
```
The following four metrics are created.
*1. cum_rev_till_prev_order: This is the cumulative revenue of a customer till previous order
*2. cumnum_prod_till_prev_order: Cumulative number of items till previous order.
*3. rev_prev_order: revenue made from previous order
*4. num_prod_prev_order: Number of items ordered from previous order

Another important metric would be number of days till last order
```{r}
order_agg <- order_agg %>% arrange(custno,prodcat1,orderdate) %>%
  group_by(custno,prodcat1) %>%
  mutate(orderdate_prev_ord = dplyr::lag(orderdate, n = 1, default = NA))

order_agg$num_days_till_last_order <- difftime(order_agg$orderdate, order_agg$orderdate_prev_ord, units="days")

order_agg$orderdate_prev_ord<-NULL

order_agg$num_days_till_last_order <-as.numeric(order_agg$num_days_till_last_order)

summary(order_agg$num_days_till_last_order)
```

The order aggregate data now looks like.
```{r}
head(order_agg,10)
```


Now lets join the above data with order_agg data (order data aggregated at order-prodcat1 level). We will join order_agg with prodcat1 on the inequality. Since we are planning to predict prodcat1, we will put order_agg on the left and perform a left join.
```{r}
joined_df<-left_join(order_agg,online_spread_e2e1cat,by="custno") 
joined_df[,13:36][is.na(joined_df[,13:36])] <- 0



joined_df$dt<- as.character(joined_df$dt)

joined_df$dt<-ifelse(joined_df$dt>joined_df$orderdate,NA,joined_df$dt)


joined_df$dt <- strptime(x = as.character(joined_df$dt),
                                format = "%Y-%m-%d %H:%M:%S")
joined_df$dt <- as.POSIXct(joined_df$dt, tz = "", format="%Y-%m-%d %H:%M:%S")

joined_df[c("session","visitor","event2_1","event2_2","event2_3","event2_4","event2_5","event2_6","event2_7","event2_8","event2_9","event2_10","event1_1","event1_2","event1_4","event1_5","event1_6","event1_7","event1_8","event1_9","event1_10","event1_11","event1_0","category_1","category_2","category_3")]<-lapply(joined_df[c("session","visitor","event2_1","event2_2","event2_3","event2_4","event2_5","event2_6","event2_7","event2_8","event2_9","event2_10","event1_1","event1_2","event1_4","event1_5","event1_6","event1_7","event1_8","event1_9","event1_10","event1_11","event1_0","category_1","category_2","category_3")], function(x) ifelse(is.na(joined_df$dt)==TRUE,NA,x))

joined_df<- joined_df %>% filter(orderdate>=dt | is.na(dt)==TRUE)
head(joined_df,20)
```
as you can see for a customer with a given orderno and prodcat1, only the online activity on or before the time of the order is joined. Now lets calculate the difference between orderdate and dt.
Note: We are also incluing the order data for which no online data is available

```{r}
joined_df$date_diff<- difftime(joined_df$orderdate,joined_df$dt,units = 'days')
head(joined_df,20)
```

We are assuming that only the last 30 days of online activity drives buying behaviour. Therefor we will only consider online activities and browsing category that occured 30 days before a transaction.

```{r}
joined_df1 <- joined_df %>% filter(date_diff<=30 | is.na(date_diff)==TRUE)
joined_df2 <- joined_df %>% filter(date_diff>30)
joined_df2[,13:36]=0
joined_df_new <- rbind(joined_df1,joined_df2)
joined_df_new[, 13:36][is.na(joined_df_new[, 13:36])] <- 0

head(joined_df_new,20)
```
What we have done above is for date difference greater than 30 days, we have changed the events flags (event2_1, event2_2 etc.) and to browsing category flags to 0 as we are not considering those events to have an impact on the buying behaviour. Now we will aggregate the data by taking the count of each events and categories. This count will be the number of times that event has happened (or browsing category used) in the past 30 days before a transaction.

Now we will aggregate the data to order-prodcat1 level

```{r}
df<- joined_df_new %>% group_by(custno,ordno,orderdate,prodcat1,cumrev_till_prev_order,cumnum_prod_till_prev_order,rev_prev_ord,num_prod_prev_ord,num_days_till_last_order) %>% 
  summarise(sum_category_1 = sum(category_1),
            sum_category_2 = sum(category_2),
            sum_category_3 = sum(category_3),
            sum_event1_1 = sum(event1_1),
            sum_event1_2 = sum(event1_2),
            sum_event1_4 = sum(event1_4),
            sum_event1_5 = sum(event1_5),
            sum_event1_6 = sum(event1_6),
            sum_event1_7 = sum(event1_7),
            sum_event1_8 = sum(event1_8),
            sum_event1_9 = sum(event1_9),
            sum_event1_10 = sum(event1_10),
            sum_event1_11 = sum(event1_11),
            sum_event2_1 = sum(event2_1),
            sum_event2_2 = sum(event2_2),
            sum_event2_3 = sum(event2_3),
            sum_event2_4 = sum(event2_4),
            sum_event2_5 = sum(event2_5),
            sum_event2_6 = sum(event2_6),
            sum_event2_7 = sum(event2_7),
            sum_event2_8 = sum(event2_8),
            sum_event2_9 = sum(event2_9),
            sum_event2_10 = sum(event2_10),
            avg_date_diff = mean(date_diff,na.rm = TRUE)
            )

head(df)
```

Another metric we can include is revenue per product for cumuative value as well as previous orders
```{r}
df$cumrev_per_prod_till_prev_order <- ifelse(df$cumrev_till_prev_order==0,0,df$cumrev_till_prev_order/df$cumnum_prod_till_prev_order)

df$rev_per_prod_prev_ord <- ifelse(df$rev_prev_ord==0,0,df$rev_prev_ord/df$num_prod_prev_ord)
df[,c('cumrev_till_prev_order','cumnum_prod_till_prev_order','rev_prev_ord','num_prod_prev_ord')]<-NULL
```


```{r}
df$avg_date_diff<-as.numeric(df$avg_date_diff)
```

Breaking down orderdate to month, quarter, day-of-week, week of the year and hour
```{r}
df$order_month<-format(df$orderdate,"%m")
df$order_week_of_year<-strftime(df$orderdate,format="%W")
library(lubridate)
df$order_qtr<-quarter(df$orderdate)
df$order_day_of_week<-weekdays(df$orderdate,abbreviate = TRUE)
df$order_hour_of_day<-format(df$orderdate,"%H")

# converting the above features to factors
df[c('order_month','order_week_of_year','order_qtr','order_day_of_week','order_hour_of_day')] <- lapply(df[c('order_month','order_week_of_year','order_qtr','order_day_of_week','order_hour_of_day')], factor)
```


We have created the folllowing features by manipulating and combining order and online data.
```{r}
head(df)
```

The summary of the data is
```{r}
summary(df)
```

###3. Feature Selection

Lets look at the correlation between cumrev_per_prod_till_prev_order and rev_per_prod_prev_ord.
```{r}

cor(df[,!names(df) %in% c("custno","ordno","orderdate","prodcat1","order_month","order_day_of_week","order_week_of_year","order_qtr","order_hour_of_day")])
```
This is a very high correlation.
```{r}
cor(df$rev_per_prod_prev_ord,df$cumrev_per_prod_till_prev_order)
```
Therefore, we will choose only one metric as a predictor, which is rev_per_prod_prev_ord.
```{r}
df$cumrev_per_prod_till_prev_order <- NULL
```

For categorical variables, we will perform the chi-square test of association. We will compare various columns derived from orderdate. 
```{r}
#"custno","ordno","orderdate","prodcat1","order_month",
chisq.test(df$order_month,df$order_qtr)
chisq.test(df$order_day_of_week,df$order_hour_of_day)
chisq.test(df$order_day_of_week,df$order_week_of_year)
```
since the p-value is < 2.2e-16 is less than the cut-off value of 0.05, we can reject the null hypothesis in favor of alternative hypothesis and conclude, that the variables are dependent to each other. Therefore, we will only consider one variable for moedeling, which is order_month and delete the rest.

```{r}
df[,c("order_day_of_week","order_week_of_year","order_qtr","order_hour_of_day")]<-NULL

#removing id columns
df[,c("custno","ordno","orderdate")]<-NULL
```
We have removed combination of highly correlated variables and highly associated variable. During the model building phase we will encounter some variables that are not significant predictors to the response variable. In those steps, we will still be performing feature selection by removing insignificant predictors and keeping significant ones.

##4. Model Designing and sampling

We have prepared the data that now we can use to fit a model. We are trying to fit a model which predicts what product category-1 is a user most likely to buy based on his past online-activity as well as his buying behaviour. We will split the data into training and test sample. We will use the training sample to fit different classification models and test sample to measure the performance of the model. The train-test split is 70-30 split, i.e., 70% of the data is used for training and 30% for testing.

```{r}
## 70% of the sample size
smp_size <- floor(0.70 * nrow(df))

## set the seed to make your partition reproducible
set.seed(1234)
train_ind <- sample(seq_len(nrow(df)), size = smp_size)

train <- df[train_ind, ]
test <- df[-train_ind, ]

```

Our response mode is prodcat1. We need to make sure that all the classes of prodcat1 are present in train and test samples
```{r}
table(train$prodcat1)
```

```{r}
table(test$prodcat1)
```

In the next section, we will use different modelling techniques to fit a multi-class classifcation models. We will use the following algorithms
*1. Logistic regression
*2. Random Forest Regression

Logistic regression works well for linear relationships and has high interpretability, whereas Random Forest can fit non-linear relationships at the cost of interpretation.

The metric we will use to determine the best model is test-AUC (Area under the curve of the ROC curve for test sample)

##5. Model Generation and Evaluation

```{r}
#remove unnecessary objects to free-up space
rm(list=ls()[! ls() %in% c("df","train","test","online","order")])
gc()
```

In this step we will fit different models on the training sample and predict for the test sample 

### Logistic Regrssion
We will fit a mutinomial logistic regression model. We will ignore num_days_till_last_order and avg_date_diff in logistic regression as they have NA values. We could impute those values but given the time constraint, we will choose to ignore them. 
```{r}
train1<- train
test1<- test
train1[,c("num_days_till_last_order","avg_date_diff")]<-NULL
test1[,c("num_days_till_last_order","avg_date_diff")]<-NULL

library(nnet)
# Fit the model
glm <- nnet::multinom(prodcat1 ~., data = train1)
# Summarize the model
summary(glm)
```

Now we'll calculate Z score and p-Value for the variables in the model.
```{r}

z <- summary(glm)$coefficients/summary(glm)$standard.errors

p <- (1 - pnorm(abs(z), 0, 1))*2
p
```

Calculating the the odds ratio coefficient for each predictor 
```{r}
exp(coef(glm))
```

Calculate Variable importance (absolute value of t-statistic)
```{r}
varimp_glm<-as.data.frame(varImp(glm))
varimp_glm$predictor<-rownames(varimp_glm)
colnames(varimp_glm)[1]<-'importance'

varimp_glm %>% arrange(desc(importance))

```
We can see that order month is the most important parameter. This is evident from the time series trends that we observed while exploring the data. Other important variables were sum_event1_8 ,sum_event1_8, and sum_event1_5 

Let's check for fitted values now.
```{r}
head(fitted(glm))
```


predicting on the test data
```{r}
predict_tst=as.data.frame(predict(glm,test1,type="probs"))
colnames(predict_tst)<-sapply(colnames(predict_tst), function(x) paste('logit_',x,sep = ""))
predict_tst$predicted_class<-apply(predict_tst,1,which.max)
predict_tst$predicted_class<-ifelse(predict_tst$predicted_class==6,7,predict_tst$predicted_class)
head(predict_tst)

#test1=cbind(test1, predict_tst)
```

Creating confusion matrix for test sample
```{r}
tab<-table(predict_tst$predicted_class,test1$prodcat1)
library(caret) 
conf<-confusionMatrix(tab)
conf
```
Class2 has high sensitivity, which means the model has a higher True Positive Rate for Class2. This means that the model does a good job of predicting whether a customer will will buy product category 2. At the same time it does a poor job of predicting whether a customer is not going to buy a product from prodcat2 or not. This is evident from the specificity of Class2

If we  we look at the sensitivity and specificity across all the other classes, we will see that the sensitivity values are low and specificity values are high. This means that, for the other classes the model does a better job identifying whether a customer is not going to buy a product in that class than predicting whether a customer is going to buy a product in that class



Calculating Test AUC of the ROC curve. The AUC is a measure of how well a model does a job of distinguishing between classes 
```{r}
library(HandTill2001)
auc(multcap(response=test1$prodcat1,predicted = predict(glm,test1,type="probs")))
```
This is a decent value. But it could be improved further by using complex models.

### Random Forest Classification


```{r}
# train1<- train
# test1<- test
# train1[,c("num_days_till_last_order","avg_date_diff")]<-NULL
# test1[,c("num_days_till_last_order","avg_date_diff")]<-NULL

library(randomForest)
# Fit the model
set.seed(1234)
rf <- randomForest(prodcat1 ~., data = train1, ntree=500, mtry=round(sqrt(ncol(train)-1)), importance=TRUE)
# Summarize the model
rf
```



Calculate Variable importance
```{r}
varImp(rf)
```
Similar to what we have observed in the multinomial logistic regression, we can see that order month is the most important predictor.


predicting on the test data
```{r}
predict_tst_rf=as.data.frame(predict(rf,test1,type="prob"))
colnames(predict_tst_rf)<-sapply(colnames(predict_tst_rf), function(x) paste('rf_',x,sep = ""))
predict_tst_rf$predicted_class_rf<-apply(predict_tst_rf,1,which.max)
predict_tst_rf$predicted_class_rf<-ifelse(predict_tst_rf$predicted_class_rf==6,7,predict_tst_rf$predicted_class_rf)
head(predict_tst_rf)

#test1=cbind(test1, predict_tst_rf)
```

Creating confusion matrix for test sample
```{r}
tab_rf<-table(predict_tst_rf$predicted_class_rf,test1$prodcat1)
library(caret) 
conf_rf<-confusionMatrix(tab_rf)
conf_rf
```
The accuracy of the model is similar to the multinomial logisitic regression. Even the sensitivity and specificity across the classes is similar to multinomial logistic regression. Class 2 has high sensitivity and low specificity and all the other classes have low sensitivity and high specificity. 


Calculating Test AUC of the ROC curve
```{r}
library(HandTill2001)
auc(multcap(response=test$prodcat1,predicted = predict(rf,test1,type="prob")))
```

The random forest model has better fit on the training data, as evident from the model summary, but it does not do a job better than multinomial logistic regression to seperate the classes. One possible reason could be that we did not choose that big of an ensemble. The number of trees that we choose in the forest were only 500. If we increase it, the performance will improve.


### Random Forest with hyper parameter tuning

We tune the hyperparameters of random forest model so that it can converge on a more optimal output. There are two hyper parameters of the random forest

*1. mtry: number of predictors randomly chosen for the decision trees in the forests
*2. ntree: total number of decision trees in the forest.

One caveat though, this process requires a lot of computation and takes some time to converge.
```{r}
levels(train1$prodcat1)<-c("cat1","cat2","cat3","cat4","cat5","cat7")
levels(test1$prodcat1)<-c("cat1","cat2","cat3","cat4","cat5","cat7")
```


```{r}
library(tidyverse)
library(caret)
library(randomForest)
customRF <- list(type = "Classification", library = "randomForest", loop = NULL)
customRF$parameters <- data.frame(parameter = c("mtry", "ntree"), class = rep("numeric", 2), label = c("mtry", "ntree"))
customRF$grid <- function(x, y, len = NULL, search = "grid") {}
customRF$fit <- function(x, y, wts, param, lev, last, weights, classProbs, ...) {
  randomForest(x, y, mtry = param$mtry, ntree=param$ntree, ...)
}
customRF$predict <- function(modelFit, newdata, preProc = NULL, submodels = NULL)
  predict(modelFit, newdata)
customRF$prob <- function(modelFit, newdata, preProc = NULL, submodels = NULL)
  predict(modelFit, newdata, type = "prob")
customRF$sort <- function(x) x[order(x[,1]),]
customRF$levels <- function(x) x$classes
```

```{r}
control <- trainControl(method="cv", number=10, #repeats=3, 
                        classProbs = TRUE)
tunegrid <- expand.grid(.mtry=c(15:18), .ntree=c(500, 1000))
set.seed(1234)
custom <- train(prodcat1~., data=train1, method=customRF, metric="ROC", tuneGrid=tunegrid, trControl=control)
summary(custom)
plot(custom)
```

I have included the code but has not run it as it takes a lot of time to run and knit the report.

##6. Summary

To summarise, we had the customer order data as well as customer online activity data. We explored the data and found out that there is a seasonality in the revenue, number of orders, as well as the online activity. It peaks during Nov and Dec and drops during the months of Feb and Oct. We also saw that this trend is consitent across browsing categories as well as differnet online events. We also found out that most of the online activity is done on browsing category 3.

We also tried associating customer order data with online behaviour. While doing so, we made an assumption  
*1. Only the last 30 days of online activity drives buying behaviour for a customer.  
Any activity before that does not affect buying behaviour significantly. Based on this assumption, we have merged the online data with the order data. We were also able to derive som metrics like, count of each online event before the purchase, Number of days since last order, order month etc. We have used this metric to predict product category-1.

The predictive problem we are trying to solve is: Based on historical purchases and online beviour, what is the likelihood that a customer would purchase a product from a product-category1. To fit and measure the performance of the model, we first split the data into training and test sample. 70% of the data is used for training and 30% for measure its performance on unseen data. We have tried multinomial logistic regression, random forest, and random forest with hyper parameter tuning. Both the models performed decent on the test data. The models are good at identifying whether a customer is not going to buy from a particular product-category. The AUC value shows that the model does a decent job of separating classes in logistic regression. To improve the performance of the random forest model, we can perform hyperparameter tuning using a grid-search approach. This process takes a lot of time and computation capacity. I have shared the code for doing that.

With a better predicitve power, we can predict with high accuracy the product category where a customer is mostly likely to shop from. We can use this information to run targeted campaign or provide incentive to buy back from us.